Review of signal distortion through metal microelectrode recording circuits and filters

Abstract

Interest in local field potentials (LFPs) and action potential shape has increased markedly. The present work describes distortions of these signals that occur for two reasons. First, the microelectrode recording circuit operates as a voltage divider producing frequency-dependent attenuation and phase shifts when electrode impedance is not negligible relative to amplifier input impedance. Because of the much higher electrode impedance at low frequencies, this occurred over frequency ranges of LFPs measured by neurophysiologists for one head-stage tested. Second, frequency-dependent phase shifts are induced by subsequent filters. Thus, we report these effects and the resulting amplitude envelope delays and distortion of waveforms recorded through a commercial data acquisition system and a range of tungsten microelectrodes. These distortions can be corrected, but must be accounted for when interpreting field potential and spike shape data.

Full text

Journal of Neuroscience Methods 169 (2008) 141–157
Review of signal distortion through metal microelectrode
recording circuits and filters
Matthew J. Nelsona,b,∗, Pierre Pouget a, Erik A. Nilsen c,1,
Craig D. Pattenc, Jeffrey D. Schalla
aCenter for Integrative & Cognitive Neuroscience, Vanderbilt Vision Research Center,
Department of Psychology, Vanderbilt University, Nashville, TN, USA
bCalifornia Institute of Technology, Pasadena, CA, USA
cPlexon Inc., Dallas, TX, USA
Received 19 September 2007; received in revised form 30 November 2007; accepted 3 December 2007
Abstract
Interest in local field potentials (LFPs) and action potential shape has increased markedly. The present work describes distortions of these signals
that occur for two reasons. First, the microelectrode recording circuit operates as a voltage divider producing frequency-dependent attenuation and
phase shifts when electrode impedance is not negligible relative to amplifier input impedance. Because of the much higher electrode impedance
at low frequencies, this occurred over frequency ranges of LFPs measured by neurophysiologists for one head-stage tested. Second, frequency-
dependent phase shifts are induced by subsequent filters. Thus, we report these effects and the resulting amplitude envelope delays and distortion
of waveforms recorded through a commercial data acquisition system and a range of tungsten microelectrodes. These distortions can be corrected,
but must be accounted for when interpreting field potential and spike shape data.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Impedance; Electrode; LFP; Phase; Frequency
Various metal microelectrodes have been designed to isolate
spikes (Green, 1958; Hubel, 1957; Levick and Cleland, 1974;
Merrill and Ainsworth, 1972; Wolbarsht et al., 1960; reviewed
by Lemon, 1984), and different metals and insulations are in
use today. An equivalent circuit model of a metal microelec-
trode in tissue has been proposed that has important theoretical
implications about frequency-dependent amplitude attenuation
(Lemon, 1984; Robinson, 1968) and phase shifts (Geddes, 1972)
of recorded signals. Such consideration in past neurophysiolog-
ical literature has been primarily given only to the recording
of spiking activity. Filtering applied during data acquisition
or offline further distorts recorded signals (Oppenheim and
Schafer, 1998). If not prevented or accounted for, such distor-
tions can introduce uncertainty into analyses of LFPs or spike
shapes. Many recent studies have described LFP phase (Bragin et
al., 1995; Haslinger et al., 2006; Lee et al., 2005; Lin et al., 2006;
∗Corresponding author at: Vanderbilt Vision Research Center, Department
of Psychology, Wilson Hall, 111 21st Avenue South, Vanderbilt University,
Nashville, TN 37203, USA. Tel.: +1 615 322 5134; fax: +1 615 343 8449.
E-mail address: matthew.j.nelson@vanderbilt.edu (M.J. Nelson).
1Present address: Cyberkinetics, Foxborough, MA, USA.
Murthy and Fetz, 1996; O’Keefe and Recce, 1993; Skaggs et
al., 1996), spike-field phase relationships (Haslinger et al., 2006;
Lee et al., 2005; Lin et al., 2006; Murthy and Fetz, 1996; O’Keefe
and Recce, 1993; Skaggs et al., 1996), event-triggered potentials
(Fries et al., 2001a,b; Kreiman et al., 2006) and LFP power or
coherence comparisons across frequencies (Fries et al., 2001a,b;
Liu and Newsome, 2006; Rickert et al., 2005; Womelsdorf et al.,
2006). However, phase distortion caused by the recording sys-
tem is rarely considered (but see O’Keefe and Recce, 1993) and
electrode-induced effects have been overlooked. Therefore, we
performed systematic measurements to verify that the equiva-
lent circuit model applies to commercial electrodes (FHC) and a
data acquisition system (Plexon) in common use by neurophysi-
ologists, and to demonstrate the signal distortions that can occur.
1. Materials and methods
1.1. Equivalent circuit model
Fig. 1 illustrates a modified version of a commonly cited
equivalent circuit model of a metal microelectrode recording in
the brain (Robinson, 1968). The effective electrode impedance
0165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jneumeth.2007.12.010

142 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
Fig. 1. Equivalent circuit model and methods. (A) Equivalent circuit model of
a metal microelectrode in the brain adapted from Robinson (1968). The entire
circuit is comprised of the electrode in the brain and the amplifier with a filter.
The effective impedance of the electrode (Z
e) is comprised of the resistance
of the electrolyte solution (Rs), the resistance and capacitance at the double
layer interface of the electrolyte and the uninsulated electrode tip (Reand
Ce) and the (negligible) resistance of the metal electrode (Rm). The effective
input impedance of the amplifier (Z
a) is comprised of the input impedance
of the head-stage amplifier (Za) and the shunt resistance and capacitance to
ground from the tip of the electrode to the input of the amplifier (Rsh and Csh).
The triangle represents an ideal amplifier that draws no current. The non-ideal
aspects of the amplifier have been accounted for in Za. Given the frequency-
dependent potential at the electrode tip (Vsig(ω)), a current (I(w)) is drawn
towards ground through the electrode and effective amplifier circuit, creating
the potential (Vin(ω)) at the input of the amplifier which is subject to the fre-
quency response of analog filters (H(w)) before being recorded (Vrec(ω)), all
according to the equation: Vrec(ω)=H(ω)[(Vsig (ω)Z
a(ω))/(Z
e(ω)+Z
a(ω))].
Thus, the microelectrode recording circuit corresponds to a voltage divider with a
frequency-dependent gain due to the filtering of H(ω) and the frequency depen-
dence of the impedances Z
eand Z
a. (B) Diagram of microelectrode testing
apparatus. Two aluminum plates were connected and separated from each by
non-conducting plastic supports, shown here from a top and side view. The appa-
ratus was immersed in dilute saline with voltage signals applied to the signal
plate with an electrode suspended from above 3 mm away. See Section 1for
more details. (C) Equivalent circuits for the parallel and series configuration.
Rsal1 is the resistance for current to travel from the signal plate to the electrode
tip in the saline, and Rsal2 is the remaining resistance for current to reach the
ground plate.
(Z
e) is the sum of impedances due to the resistance of the elec-
trolyte (Rs), the resistance of the electrode metal (Rm) and,
most importantly, the resistance and capacitance at the dou-
ble layer that forms at the electrode/electrolyte interface at the
uninsulated electrode tip (Reand Ce). The effective amplifier
input impedance (Z
a) is the total impedance to ground past the
electrode; this includes a path through the first amplifier, or head-
stage (Za), and shunting routes to ground outside the amplifier
(Rsh and Csh) which are typically capacitive. This shunt capac-
itance arises mainly from the capacitance across the insulation
between the electrode shaft and the surrounding electrolyte as
well as the cumulative capacitance along cables and connec-
tors between the electrode and head-stage amplifier (Robinson,
1968). These routes to ground parallel to the amplifier reduce the
effective amplifier impedance, and being capacitive, this effect
increases with signal frequency.
Signals at the tip of the electrode (Vsig) generate currents
(I) that flow to ground through the series combination of the
effective electrode impedance and the effective amplifier input
impedance
I(ω)=Vsig(ω)
Z
a(ω)+Z
e(ω)(1)
The voltage at the input of the amplifier (Vin)isgivenby
Vin(ω)=Vsig (ω)−I(ω)Z
e(ω)=Vsig(ω)Z
a(ω)
Z
a(ω)+Z
e(ω)(2)
Eq. (2) shows that Z
aand Z
eform a voltage divider so that
when Z
ais not substantially larger than Z
e,Vin will be less than
Vsig. This signal attenuation will be accompanied by a phase shift
between Vsig and Vin because Z
aand Z
eare complex values with
phases and magnitudes. When multiplying and dividing complex
numbers, phases are respectively added and subtracted indepen-
dently of the numbers’ magnitudes, while the phase of a complex
sum is the phase of the separately summed real and imaginary
fractions weighted by the magnitudes of each number, so that
larger numbers contribute more to the phase of the resulting sum.
Therefore the phase difference between Vsig and Vin equals the
phase of the effective input impedance Z
aminus the phase of
the combined impedance Z
a+Z
e. When Z
ais much larger than
Z
ethe phase of the combined impedance is dominated by the
phase of Z
a, so the resulting phase shift will be negligible. When
this is not the case, potentially noticeable phase shifts will occur
and will increase in size as both the relative magnitude of Z
eto
Z
aincreases and the overall phase difference between Z
eand
Z
aincreases. The direction of the phase shift will depend on
whether Z
eis more or less capacitive than Z
a, resulting in pos-
itive or negative going phase shifts, respectively. For example,
if Z
ewas purely capacitive (phase= −90◦) and Z
awas purely
resistive (phase = 0◦), then when the magnitudes of Z
aand Z
e
are approximately equal, the phase of Vin relative to Vsig would
be about 45◦, indicating that Vin would lead Vsig by this amount.
This phase shift would increase towards an asymptote of 90◦as
Z
ebecomes larger than Z
a. Note that because Z
aand Z
eare
functions of frequency, the magnitude and phase relationship
between Vsig and Vin will be frequency-dependent.
It is worth noting that only the first amplifier’s input
impedance is critical for the measurement, as this is the only
amplifier that interacts with the electrode and affects the possi-
bly considerable voltage drop that may occur across it. At this
stage, the initial amplifier sets its voltage using its electrical
power source based on its gain and the signal input to it, with

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 143
the limitation that it cannot set a voltage larger than the voltage of
its power source. That signal is then sent to following amplifiers
and/or recording equipment, and at each stage an additional pos-
sible voltage divider is created involving the output impedance
of the preceding stage and the input impedance of the following
stage. However, no further signal distortion typically occurs at
these stages as the input impedance of these stages can usually
easily be set well above the output impedance of the preceding
stage.
1.2. Filtering effects
Physiological data acquisition systems include filters that will
affect signals in a manner described by the transfer function of
the system (H(ω)) such that
Vrec(ω)=H(ω)Vin (ω)=H(ω)Vsig(ω)Z
a(ω)
Z
a(ω)+Z
e(ω)(3)
Any filter, analog or digital, that could be applied in real
time during data acquisition would necessarily introduce some
frequency-dependent phase shifts that become large near the
filter’s passband edges. However, once data acquisition has
stopped it becomes possible to re-apply the same filter to time
reversed data which imposes exactly the same phase shifts intro-
duced during acquisition but in the opposite direction, thus
correcting the phase shifts applied during acquisition. This forms
the basis for phase shift-free filters that may be applied in post-
acquisition processing (Mitra, 2001).
1.3. Data collection procedures
Signals were recorded using a MAP system (Plexon Inc., Dal-
las, TX) in which signals were passed through a first and second
amplifier, which we refer to as a head-stage and a preampli-
fier, respectively, following the convention of the company that
constructed it. After the amplifiers, signals are passed to a mul-
tichannel acquisition processor (MAP) for A–D conversion and
recording. At the stage of the preamplifier, each input chan-
nel is separated into two output channels that undergo different
analog filtering, with one channel designed to record higher fre-
quency spikes and one designed to record lower frequency field
potentials, which we refer to as the spike and LFP channels,
respectively. In this article, when the outputs from both chan-
nels are not overlaid, values shown in plots at and below 175 Hz
were obtained from the LFP channel data, and values at and
above that were obtained from spike channel data as indicated
on the plots. Taken together, the two outputs enabled us to per-
form measurements across the entire frequency range of interest,
and for those frequencies that could be measured through either
channel (∼80–300 Hz), the results from each channel were the
same.
Most of the data presented in this study was recorded with a
HST/8 o50-G20 (Rev 3.0) head-stage (Plexon Inc., Dallas, TX)
with a gain of 20, which we refer to as the low input impedance
head-stage (38 Minput resistance with 3 pF of parallel capac-
itance and 10 pF of series capacitance acting on the input before
amplification). This was used with a following preamplifier with
a gain of 50 (Plexon Inc., Dallas, TX). The preamplifier was con-
figured as a PBX2/16sp/16fp preamplifier with two cascaded
1-pole low-cut Butterworth filters and a 4-pole high-cut Butter-
worth filter for each of 16 spike channels (100 Hz–8 kHz) and 16
field potential channels (0.7–170 Hz). Additional filtering by the
MAP system’s SIG board causes the effective low-cut frequency
of the recorded spike channels to be ∼250 Hz. Unless otherwise
specified, all data presented in this study was recorded with this
equipment.
Different head-stages and preamps were used in some record-
ings to determine the effects of different equipment. We tested
a second head-stage (Plexon Inc., Dallas, TX) with a gain
of 1, HST/8o50-G1-GR, which we refer to as the high input
impedance head-stage (>1 Ginput resistance with ∼2pF of
parallel input capacitance and no series capacitance). This was
primarily used with a PBX2/16sp/16fp preamplifier (Plexon
Inc., Dallas, TX) with a gain of 1000 but with the same LFP
and spike channel filters as the primary preamplifier mentioned
above. We also obtained the phase response of the LFP channel
of a second preamplifier for signals up to 300 Hz passed directly
to the high input impedance head-stage across no resistance. This
preamplifier was configured as a PBX/16sp-r-G50/16fp-G50
preamplifier (Plexon Inc., Dallas, TX) with 16 spike chan-
nels (spike data not shown) and 16 field potential channels
(1-pole Butterworth filters, cut-offs of 3.3–88 Hz). Because
this configuration resulted in an overall gain of 50 between
the head-stage and preamp instead of an overall gain of 1000
that occurred with all other recordings, larger voltage signals
were tested with this combination of equipment to compensate,
though all other equipment and procedures were kept the same.
The resulting data from this test is shown in the grey line in
Fig. 7.
The MAP unit can also record additional analog signals via
BNC inputs on a separate card (National Instruments, TX). This
was used to record the actual non-attenuated voltage signal as
well as the spike channel data as a continuous signal using the
OUT board of the MAP unit. The LFP channel was automatically
recorded by this same equipment, and thus all three signals for
analysis in this study (actual signal, spike channel, and LFP
channel) were time-stamped and recorded simultaneously by the
same equipment. The sampling rate used for all recordings was
20 kHz. Channel 1 was used for all recordings, and the inputs to
unused channels were grounded.
Most voltage signals used in this study were generated by
clipping onto the audio output pin of a computer playing Matlab
generated .wav files. This allowed us to present arbitrary sig-
nals to the system and to reproduce with ease precisely the same
signal at many frequencies across different conditions. Distor-
tions introduced by the audio card of the computer qualitatively
seemed small for most signals, and were unimportant to the
conclusions of the study as we were able to record the actual
output signal in all cases. In order to generate signals of the
appropriate amplitudes for use with the neural recording equip-
ment, signals were first attenuated by a factor of about 100 by
being passed through a voltage divider constructed by connect-
ing a 100-and 1-resistor in series, with the exception of the

144 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
few tests that were performed with the secondary preamplifier
using larger and unattenuated voltages. Some later tests were
performed using sinusoidal signals created by a function gen-
erator (33220A function/arbitrary waveform generator, Agilent
Technologies, Santa Clara, CA). Output signals from this were
still initially routed through the same voltage divider.
To verify amplifier input impedance, the attenuated signal
was passed directly to the head-stage connector or passed across
resistors with impedances varying from 11.5 to 88 Mfor the
low input impedance head-stage. For the high input impedance
head-stage, low frequency signals were passed across very high
metallic resistances ranging from 0.5 to 2.5 Gwhile moder-
ate to higher frequency signals were passed across moderate
resistances ranging from 1.2 to 66.0 M. See Section 1.5 for a
description of how the amplifier input impedance was assessed
using this data.
For the electrode data, an apparatus was constructed con-
sisting of two square 7 in. ×7 in. aluminum plates connected
together by two plastic supporting rods causing a plate separa-
tion of 7 in. A coarse schematic of the apparatus can be seen
in Fig. 1B. The plates were connected with their broad sides
facing each other and they stood on their thin edge in a large
plastic tub filled with either dilute saline with a concentration of
0.225% by weight or physiological saline with a concentration
of 0.9% by weight. By passing current between the plates, a
one-dimensional voltage gradient was created in the dimension
normal to the plates’ broad sides. Voltage changed with the hor-
izontal position between the two plates but was approximately
uniform in the two directions orthogonal to this: the vertical
direction and the horizontal direction parallel to the plates. The
dilute saline was initially chosen as its higher resistivity allowed
for a better control of this gradient. Later recordings were made
with both saline concentrations to investigate potential effects
of saline concentration on the electrode tip impedance.
To provide a verification of the equivalent circuit model, data
was collected under two configurations. In the parallel configu-
ration, the attenuated signal was connected to one plate, which
we define as the signal plate, with the other plate connected
to ground, which we call the ground plate. In this case, when
the electrode tip is immersed in the saline it provides a high
impedance route to ground from the signal plate that is parallel
to a lower impedance route through the ground plate. The actual
voltage gradient in the saline will primarily be unaffected by
the presence or the position of the electrode. This is generally
analogous to the case of neural recording. In the series config-
uration, the ground plate is disconnected from everything, so
that the electrode would be the only series connection between
the signal plate and ground and thus all current in the signal
passing through the aluminum plate must pass through the elec-
trode and amplifier circuit as well. Resistance between the two
plates was measured before and after each recording session and
found to be around 100–200 . At the start of a session the resis-
tance was occasionally larger than this, in which case we sanded
down both plates’ surfaces which served to lower the impedance
to the appropriate level, most likely by removing aluminum
oxide or possibly solid sodium chloride that had formed on the
plates.
The electrodes used for data collection solely in the dilute
saline with the low input impedance head-stage were 5 tung-
sten microelectrodes (FHC, Bowdoinham, ME) 3 insulated with
glass and 2 with epoxylite, with varying impedances ranging
from 0.5 to 9.8 Mat 1 kHz as per the manufacturer specifi-
cations. We tested an additional epoxylite-insulated electrode
with a manufacturer specified impedance of 8.4 Mat 1 kHz
using only the high input impedance head-stage in dilute saline.
The FHC catalog numbers for the 5 electrodes used with the
low input impedance head-stage were: UEWLGASEBN1E,
UEWLGASEFN1E, UEWLGASGBN4E, UEWLGASGDN4E
and UEWLGASGFN4E, and the catalog number for the elec-
trode used with only the high input impedance head-stage
in dilute saline was UEWLGASEFN1E. We later tested 3
additional epoxylite-insulated electrodes with manufacturer
specified 1 kHz impedances ranging from 0.5 to 10 Mwith
both head-stages and in dilute and/or physiological saline. The
catalog numbers for these electrodes are: UEWLGASEBN1E,
UEWLGASEDN1E and UEWLGASEFN1E. The order in
which the tests were performed for both head-stages and saline
concentrations was varied for each of these electrodes. Through
the course of the experiment the impedance of each electrode
was independently measured (see Figs. 3C, 4C and 6B), and the
tests conducted in physiological saline matched reasonably well
with the manufacturer specified values (see Fig. 6B). The tip
geometry was not varied across electrodes.
Using a surgical micromanipulator clamping onto a single
channel microdrive (FHC, Bowdoinham, ME) electrodes were
suspended from above and lowered to a vertical position 100␮m
below the saline surface at a horizontal position between the two
plates 3 mm away from the signal plate. The horizontal distance
from the signal plate was set by using the surgical microma-
nipulator to very carefully touch the side of the electrode to the
plate as determined by careful visual inspection, then advancing
it 3 mm away from the plate. The depth of the saline surface was
determined through online viewing of the signals recorded by
the amplifier while adjusting the electrode depth with the micro-
drive to determine when electrical contact was consistently first
made between the electrode and the saline. The electrode was
then lowered with the microdrive 100␮m beyond that point for
data collection. We compared the data recorded from each elec-
trode to data recorded from a specially constructed steel pin
reference electrode with 500 ␮m of uninsulated tip and negli-
gible tip impedance. This reference electrode was suspended
600 ␮m below the saline surface, with the horizontal position
and other conditions kept the same to obtain an estimate of the
actual voltage presented to each electrode, accounting for any
effects of the aluminum plates and saline. Data was collected
close to the signal plate so that the recorded voltages would be
as large as possible while maintaining a small voltage gradient
which resulted from the small output voltages used along with
the large horizontal separation between the plates. The small
voltage gradients were desired to help diminish the effects of
variables that could not be reproduced between electrodes with
exact precision, such as the orientation and horizontal posi-
tion of the electrode. Recordings of sinusoidal voltages at a
few frequencies were conducted after each recording session

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 145
for each electrode to ensure that the electrode’s impedance was
not affected by the signals applied during the session. Only small
apparent impedance drops were noticed on occasion.
During data collection with the electrodes and the low
impedance head-stage, Z
awas manipulated by clipping onto
the connection between the electrode and the head-stage and
connecting that to ground through different metallic resistors
with known impedances (Rsh in Fig. 1A). This created an addi-
tional parallel route to ground downstream of the electrode tip
and lowered Z
aby a known amount. This was done in both the
parallel and series configurations to create the additional 10 Hz
Z
avalues of approximately 2, 8 and 14 Min addition to the
un-manipulated value of 38 M.
For the electrodes tested in both concentrations of saline,
additional impedance measurements were made using a com-
mercially available LCR meter (E4980A, Agilent Technologies,
Santa Clara, CA), which is an instrument that can measure
inductance (L), capacitance (C) and resistance (R). Measure-
ments were made in the 4 terminal paired configuration with the
high potential and current leads ultimately connected to the plate
near the electrode, and the low potential and current leads ulti-
mately connected to the top of the electrode. All other leads to
the aluminum plates were disconnected while this measurement
was made. In addition to these tests, a corroborating impedance
measurement at 1 kHz was made using a 1-kHz metal electrode
impedance tester (Model Imp-1, Bak Electronics, Mount Airy,
MD).
1.4. Signals used
The bulk of the data for this study was gathered using sinu-
soidal voltages with frequencies varying from 0.5 Hz to 9 kHz.
The exact frequencies (in Hz) tested that underlay the data shown
in each figure are: .5, 1, 2.5, 5, 10, 15, 20, 25, 30, 40, 50, 60, 70,
80, 90, 100, 125, 150, 175, 200, 250, 300, 500, 1000, 1500, 2000,
2500, 3000, 3500, 4000, 4500, 5000, 6000, 7000, 8000 and 9000.
The amplitudes of most of the unattenuated signals were kept
approximately constant with a peak amplitude of ∼320 mV for
the metallic resistor data and ∼200 mV for the electrode data. For
situations in which the resulting signals were too small to record
reliably because of the combined effects of filters and resistors
or electrodes, signal amplitudes were increased to improve the
signal to noise ratio in order to better determine the recorded
phases and amplitudes. Every data point analyzed however was
considered only in terms of the gain relative to the applied volt-
age which was also recorded, so the absolute voltage of the
signals was unimportant.
The amplitudes used to record electrode data thus corre-
sponded to voltages of less than 2 mV at the electrode tip.
Evoked potentials recorded in cortex with microelectrodes have
been published with maxima that exceed this (Kandel and
Buzs´
aki, 1997), although physiological values at higher frequen-
cies resulting from action potentials typically do not reach this
level. Current density is known to affect electrode impedance
when the current density exceeds a certain level (Geddes et al.,
1971), but our estimations suggest that with the equipment and
signals we used, current densities were well below this level.
Additionally, we verified at a few frequencies that electrode
and amplifier impedance do not appreciably change with cur-
rent amplitude for the signals and equipment we used (data not
shown). This suggests that for physiological recordings with any
reasonable equipment, any distortions that occur will not depend
on signal amplitude appreciably.
The amplitude and phase of the digitized recorded signals
were measured in two ways, each using 50 cycles of the data.
For most recordings, the nlinfit function in Matlab (vs 2007b,
Mathworks Natick, MA) was used to find the best sine wave fit
given the known frequency of the sinusoid. In some cases the
Hilbert transform was used instead, defining the amplitude as
the average magnitude of the Hilbert transform and defining the
phase as the phase of the first sample resulting from a linear fit
of the complex phase of the Hilbert transform. The code used
for each method is provided in the Supplementary materials.
Amplitude ratios and phase comparisons between the recorded
and actual signals were always made using the same method for
each signal. For more details, see the Supplementary methods
online.
For the verification of group delay with data, passband filtered
pulse signals with different center frequencies were used, simi-
lar to what is shown in example 5.1 of Oppenheim and Schafer
(1998). A few examples of signals used are shown in Fig. 9. The
center frequencies of the filters used also varied from 0.5 Hz to
9 kHz while the duration of the signal itself decreased with fre-
quency to allow for more precise temporal localization of the
smaller group delays at higher frequencies. The filter and dura-
tion specifications were determined to provide the best frequency
localization for each signal, given that the amplitude envelope
varied sharply enough over time to determine the delay between
the two envelopes at each frequency. The filtered pulses used
were obtained by windowing sinusoids of the given carrier fre-
quency with the first of the discrete prolate spheroidal sequences
with a time-bandwidth product of 1 for a given duration. The
maximum voltages of the filtered pulses used for each record-
ing session approximately matched the voltage amplitude of the
sinusoidal signal used for each frequency in the same session.
For these signals, we used the magnitude of the Hilbert trans-
form, which can be thought of as the instantaneous amplitude
of a time series (Marple, 1999a), as an estimation of the ampli-
tude envelope for both the recorded and actual signal. We then
determined the amplitude envelope delay to be the time delay
at which the cross-correlation between the actual and recorded
envelope estimates was maximal. For our data this gave results
exactly similar to a previously published method of estimating
group delay that we later found (Marple, 1999b) in which the
order in which the cross-correlation and Hilbert transform were
applied was reversed from what we have presented here.
For the shape distortion data, we used a voltage shape
obtained from a single neuron’s recorded waveform, as well as a
frequency-modulated version of the same waveform with signal
power concentrated in the LFP frequency ranges. The original
waveform had a duration of 1 ms, which was temporally modu-
lated to have a duration of about 25 ms in the lower frequency
version. Properties of the computer’s audio card did distort the
lower frequency waveform somewhat, but, again, because we

146 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
were able to record the actual voltage applied this was unim-
portant as to our purpose of demonstrating shape distortion by
the recording equipment. The insets of Fig. 10 A and B show an
estimate of the power-spectral density of the actual signals sent
using a Fourier transform windowed with the first of the discrete
prolate spheroidal sequences with a time-bandwidth product of
1 for the duration of the signal. Also, to demonstrate a recording
of high frequency spikes recorded simultaneously with lower
frequency field potentials, we also used the same passband fil-
tered pulse signals that were used to verify the group delay, but
with the high frequency spike waveform added at the highest
central peak of the signal. These signals were recorded using
one electrode with a 1-kHz impedance verified to be 3.3 M
using the 1-kHz metal electrode impedance tester. For the pre-
sentation of this recorded data, the system’s LFP channel output
is displayed with the Spike channel added to it around the time
of the spike.
The variance of all the measurements performed in this study
was negligible, provided that all electrical connections were ade-
quately made and left undisturbed between measurements and
that the signal amplitudes used for measurements with elec-
trodes were kept sufficiently low to avoid affecting electrode
impedance. To estimate the variance that occurs while chang-
ing electrical connections, we performed measurements with
one low impedance electrode at 50 Hz several times while alter-
nating connections between the low and high input impedance
head-stages and the corresponding following amplifiers between
each measurement. There was somewhat more variance in the
high input impedance head-stage measurements than the low
input impedance head-stage. High input impedance head-stage
measurements had a range of the raw gain spanning 5.3%
of the maximal value, while the low input impedance head-
stage measurements had a range of the raw gain spanning
only 0.3% of the maximal value. There was no systematic
trend in the value of the impedance across these measure-
ments, suggesting that electrode impedance was not altered by
them.
1.5. Impedance calculations
To determine the effective amplifier input impedance, calcu-
lations were made using the amplitude ratio (Vrec/Vsig ), which we
refer to as the gain, observed in the metallic resistor data across
all frequencies. To remove the effects of analog filters, the gain
for each recording was divided by the same signal’s gain in the
reference recording where the signal was applied directly to the
head-stage using no resistors at all. We refer to this value as the
normalized gain, or here as V
rat.V
rat along with the magnitude of
the known metallic resistance the signal was sent across, which
in this case is Z
e, can be used to calculate the effective input
impedance of the head-stage as Z
a=(V
ratZ
e)/(1 −V
rat). This
is a rewritten version of Eq. (2) using V
rat in place of Vrec/Vsig ,
and considering Vrec and Vsig to be the raw gain of the metallic
resistor and reference recording, respectively.
To determine the effective electrode impedance, this same
procedure was followed with electrode recordings to obtain V
rat,
using the gain of the steel pin recordings as the reference record-
ing to remove any effects caused by the saline or aluminum plates
in addition to removing effects caused by the analog filtering.
This along with the known magnitude of Z
awas used to cal-
culate the effective electrode impedance at each frequency as
Z
e=Z
a(1/V
rat −1), which is again a rewritten version of Eq.
(2) and the equation above.
We report the value calculated for all the individual Z
avalues
tested for one electrode (Fig. 3) in addition to the averages for
the parallel and series configurations across the 4 tested values
of Z
afor several electrodes (Fig. 4). In reporting averages of
electrode impedance measurements in each configuration, a few
outlying recordings were discounted for some electrodes.
1.6. Phase calculations
The measured phase shift for each recording was defined as
the phase of the recorded signal minus the phase of the actual
signal, so that a positive phase referred to the recorded sig-
nal leading the actual signal. The phases were plotted using
the unwrap function in Matlab to provide a seemingly con-
tinuous phase response across frequencies. Since the precise
value of the phase is ambiguous since a phase curve is equiva-
lent to the same curve shifted by any multiple of 360◦,0
◦was
defined so that the phases for the most frequencies within the
passband of each channel’s filters were closest to 0◦. For the
presentation of electrode-amplifier circuit-induced phase shifts
in Figs. 5 and 6, the filter-induced reference phase shown in
black in Fig. 7 was subtracted from the raw recorded phase
shift with each electrode to remove the common filter-induced
phase effects and leave only the phase shifts resulting from the
electrode-amplifier circuit. The filter-induced reference phase
was obtained from the recorded phase shifts of signals sent
directly into the head-stage and was comprised of data collected
from both the low and high input impedance head-stages as both
were used with following preamplifiers with identical specified
filter properties. The data above 10 Hz were recorded using the
low impedance head-stage, and the data at and below 10Hz
were recorded with the high impedance head-stage which has
no series capacitance acting before amplification that introduces
additional phase shifts in this frequency band. For the electrode
data collected with the high input impedance head-stage, the
high input impedance reference phase data was subtracted over
the entire frequency range recorded to produce the orange curves
in Fig. 5.
To calculate group delay, the derivative of the phase with
respect to frequency is approximated using the change in phase
and frequency between each pair of consecutive frequency
points explicitly measured. Group delay was then calculated
according to the equation below
Group delay f1+f2
2=−
Ph
360 /f (4)
Ph is the difference in phase between adjacent frequencies
measured in units of degrees, fis the difference in frequency
in units of Hz, f1and f2are the frequencies of the consecutive
measurements used in the calculation, and group delay is given
in units of seconds. The group delay measurement using each

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 147
pair of consecutive frequencies is defined as pertaining to the
group delay observed at the mean of the two frequencies.
2. Results
2.1. Determination of amplifier input impedance
To verify that the equivalent circuit model applies to micro-
electrode recordings, we measured the input impedance for
two head-stages, one with lower and one with higher input
impedance. To do this we measured Vrec with Vsig consisting
of sine wave voltages (0.5Hz–9 kHz) applied to the head-stage
across different metallic resistances. Fig. 2 plots measurements
made with the lower input impedance head-stage through a range
Fig. 2. Measurement of effective amplifier input impedance. Plots show ampli-
tude data from signals sent directly to the low input impedance head-stage across
different metallic resistors (Rm). Line colors are coded from grey to red based
on the magnitude of Rm, with the precise values for each line indicated in A.
Spike and LFP channel data (see Section 1) are shown overlapping in A, but in
B and C the vertical dashed line denotes the point where data to the left corre-
sponds to the LFP channel data only, and data to the right corresponds to the
spike channel data only. Frequency is shown on a log scale. For a list of the exact
frequencies tested, please see Section 1.4. (A) Raw gain of the recorded over the
actual signal. (B) Normalized gain showing the voltage attenuation across the
resistor. This plot shows the raw gains in A for each recording with a greater than
zero resistance divided by the raw gain of the reference recording, which was
the recording in which Rmwas zero. (C) Effective amplifier input impedance
calculations derived from the above data for each trace. The green dashed line
represents the reported value of the amplifier alone.
of metallic resistors. The variation of gain (Vrec/Vsig) through
the LFP and spike channels as a function of frequency and
resistance is clear (Fig. 2A). By normalizing the gain for each
resistor by the gain for signals applied directly to the head-
stage, the filter properties of the system were removed (Fig. 2B).
The normalized gain allows us to calculate the effective input
impedance of the head-stage for each resistor (Fig. 2C). The
input impedance we measured corresponds to the specifications
of this head-stage. The parallel input capacitance of the head-
stage causes the input impedance to decrease at high frequencies;
the series capacitance causes it to rise at very low frequencies.
The impedance measurements are largely independent of the
resistive load and match well with the specified values, except
at high frequencies where our measurements are consistently
low, suggesting an added voltage drop across these resistors.
However, this is expected given the presence of the capacitance
shunting the amplifier, Csh. These deviations from the specified
input impedance at high frequency permit an estimation of Csh
which measured ∼2.7 pF in our recording setup. It is impor-
tant to note that this value can change for the same equipment
according to its physical arrangement.
We also tested a head-stage with a higher input impedance
which we empirically verified in a similar fashion. Due to the
very high input resistance, the effective input impedance for this
head-stage was largely determined by the capacitance within and
outside the amplifier for most frequencies. For low frequencies,
we verified there was little voltage drop over very high metallic
resistances, while for moderate to higher frequencies we verified
that there was little voltage drop over moderate resistances.
2.2. Equivalent circuit verification and signal attenuation
After determining the input impedance of the amplifier (Z
a),
we determined whether the equivalent circuit describes sig-
nals recorded through metal microelectrodes immersed in dilute
saline, using the apparatus depicted in Fig. 1B. This was done
in a parallel configuration and a series configuration (Fig. 1C,
see Section 1). If the equivalent circuit model is correct, then
measurements of electrode impedance should be independent
of both the configuration and the value of Z
a.
Fig. 3 plots measurements made with the lower input
impedance head-stage through a representative high impedance,
glass-insulated electrode. Systematic variation of raw (Fig. 3A)
and normalized (Fig. 3B) gain (Vrec/Vsig ) through the LFP and
spike channels was observed as a function of frequency and Z
a
with slightly higher gain in the series than in the parallel con-
figuration. This is to be expected because more total current
travels through the saline in the parallel configuration, resulting
in a larger voltage drop from the signal plate to the electrode
tip. The normalized gain at the various values of Z
aafforded
calculation of the effective electrode impedance as a function
of frequency (Fig. 3C). Electrode impedance measured across
signal frequencies did not vary with Z
afor either parallel or
series configurations. This constancy was found for all elec-
trodes tested. Thus, the equivalent circuit was verified.
The same pattern of results was obtained for electrodes
spanning impedance values from 0.5 to 9.8 M(manufacturer

148 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
Fig. 3. Measurement of effective electrode impedance for one electrode. Plots
show amplitude data from signals recorded with one high impedance glass-
insulated electrode in dilute saline using different manipulated values of Z
awith
the low input impedance head-stage. Line colors are coded from grey to blue
based on the value of Z
aat 10 Hz, with the precise values for each line indicated
in A. Parallel configuration data is shown with solid lines, series configuration
data is shown with dashed lines. Spike and LFP channel data (see Section 1)
are shown overlapping in A, but in B and C the vertical dashed line denotes the
point where data to the left corresponds to the LFP channel data only, and data
to the right corresponds to the spike channel data only. Frequency is shown on
a log scale. For a list of the exact frequencies tested, please see Section 1.4. (A)
Raw gain of the recorded over the actual signal. (B) Normalized gain showing
the voltage attenuation across the electrode, given by the value in A for each
recording divided by the raw gain of the reference recording, which was done
with a steel pin with negligible impedance. (C) Effective electrode impedance
(Z
e) calculations derived from the above data for each trace. Z
eis shown on a
log scale.
specified at 1 kHz) (Fig. 4). Beyond extending the verification
of the equivalent circuit, it is also clear that electrode impedance
increased substantially with decreasing frequency, and was
10–45 times higher at 10 Hz than at 1KHz, consistent with pre-
vious reports (Lemon, 1984; Merrill and Ainsworth, 1972). Note
that the rise in electrode impedance at low frequencies is not just
a result of a constant capacitance across frequencies since Reand
Ceare generally considered to be frequency-dependent them-
selves (Ferris, 1974; Robinson, 1968), which is supported by our
calculations of Reand Ce(Figure S1, see Supplementary results
online) that rely on the recorded amplitudes and phase shifts with
Fig. 4. Voltage attenuation and impedance measurements for several electrodes.
Plots show amplitude data from signals recorded with electrodes in dilute saline.
Grey-to-blue lines show data recorded using the low input impedance head-
stage for electrodes with low-to-high measured impedance values at 10Hz. The
manufacturer specified 1 kHz impedance value for each electrode is indicated in
A. Values in italics and followed by an asterisk denote data from a glass-insulated
electrode. Orange lines show data recorded with the higher input impedance
head-stage for one electrode with a large specified 1 kHz impedance of 8.4M.
Parallel configuration data is shown with solid lines, series configuration data is
shown with dashed lines. A and B denote parallel configuration recordings with
no Z
amanipulations, and C shows the average parallel and series configuration
values across 4 different values of Z
a. Spike and LFP channel data (see Section
1) are shown overlapping in A, but in B and C the vertical dashed line denotes
the point where data to the left corresponds to the LFP channel data only, and
data to the right corresponds to the spike channel data only. Frequency is shown
on a log scale. For a list of the exact frequencies tested, please see Section
1.4. (A) Raw gain of the recorded over the actual signal. (B) Normalized gain
showing voltage attenuation across the electrode, givenby the value in A for each
recording divided by the raw gain of the reference recording, which was done
with a steel pin with negligible impedance. (C) Effective electrode impedance
(Z
e) calculations derived from the above data for each trace. Z
eis shown on a
log scale.
each electrode and our estimation of Z
a. As a consequence of the
frequency dependence of the electrode impedance, the effective
amplifier gain was much less at the lower frequencies. We have
also confirmed this in the brain with simultaneous recordings of
electrodes with different impedances in the same approximate
brain location (Nelson et al., 2006). Tungsten microelectrodes
commonly used for isolating single spikes are typically 2–3 M

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 149
at 1 KHz. Thus, considerable attenuation of LFP frequency sig-
nals can occur when such electrodes are used with this lower
impedance head-stage.
The orange lines in Fig. 4 show results using the higher
impedance head-stage with one high impedance electrode, with a
manufacturer specified impedance of 8.4 M. We can see that no
considerable attenuation occurs with this electrode, as the nor-
malized gain (Fig. 4B) is close to one over the entire frequency
range tested.
2.3. Electrode-amplifier circuit-induced phase shifts
Besides amplitude attenuation, the equivalent circuit of
microelectrode recordings shows that signals will also be dis-
torted through frequency-dependent phase shifts. We measured
the phase of Vin relative to the phase of Vsig as a function of fre-
quency for signals sent across electrodes of different impedances
by subtracting the phase shifts induced by the acquisition sys-
tem’s filters alone from the phase shifts of the same sinusoidal
signals recorded with electrodes (Fig. 5A). Marked phase shifts
occurred when using the lower impedance head-stage for signals
below 100 Hz where electrode impedance was higher, and were
greater overall for higher impedance electrodes. These phase
shifts are positive in direction at lower frequencies and exceed
80◦in our data, which in conjunction with the estimated elec-
trode impedance magnitudes suggest that the phase angle of the
electrode impedances are nearly a full −90◦over these frequen-
cies for some electrodes (Figure S1, see Supplementary results
online). At higher frequencies the phase shifts shown in Fig. 5
reverse in direction, becoming slightly negative, suggesting that
Z
ais more capacitive than Z
eat these frequencies because of the
shunt and parallel amplifier input capacitance. The phase shifts
recorded with the steel pin reference electrode shown by the
dashed grey line for this head-stage are sizeable below 10 Hz,
primarily resulting from the series capacitance within the head-
stage acting on the input before amplification. This would thus
partly contribute to the phase shifts recorded with other elec-
trodes at those frequencies, though for most electrodes these
phase shifts would be large even without this contribution. The
phase shifts also increase in magnitude as Z
adecreases (Fig. 6B)
as described above, following the predictions of the equivalent
circuit.
The orange lines in Fig. 5A again shows results using
the higher impedance head-stage with one high impedance
electrode, demonstrating that like the attenuation, no electrode-
amplifier circuit-induced phase shifts occur with this head-
stage.
2.4. Saline concentration effects
After recording data in dilute saline, we were interested in
determining if the effects we have shown are qualitatively or
quantitatively different in physiological (0.9% by weight) saline.
From a careful inspection of Figs. 3 and 4, it is apparent that
though our measurements are consistent with each other, they
are noticeably higher than the manufacturer specified impedance
values. To reconcile this, we made independent impedance mea-
Fig. 5. Electrode-amplifier circuit-induced phase shifts using electrodes. All
phase shifts are shown after subtracting the phase shifts induced by the system
filters (see Fig. 8). A positive phase means that the recorded signal leads the actual
signal. Frequency is shown on a log scale. For a list of the exact frequencies
tested, please see Section 1.4. The vertical dashed lines denote the points on
each plot where data to the left corresponds to the LFP channel data and data
to the right corresponds to the spike channel data. (A) Phase shifts for signals
recorded using different electrodes in the parallel configuration in dilute saline.
Grey-to-blue lines show data recorded using the low input impedance head-
stage for electrodes with low-to-high measured impedance values at 10Hz. The
manufacturer specified 1 kHz impedance value for each electrode is indicated.
Values in italics and followed by an asterisk denote data from a glass-insulated
electrode. Orange lines show data recorded with the higher input impedance
head-stage for one electrode with large high-frequency impedance. The dashed
lines in grey and orange show the phase shifts for the steel pin reference electrode
used with the low and high impedance head-stages, respectively. (B) Phase
shifts for signals recorded with a low impedance epoxylite-insulated electrode
in the parallel configuration in dilute saline with the low impedance head-stage
while manipulating Z
a. Line colors are coded from grey to blue based on the
manipulated value of Z
aat 10 Hz, with the precise values indicated.
surements using a commercially available LCR meter and a
1-kHz metal electrode impedance tester (see Section 1) for sev-
eral electrodes in both saline concentrations. This was done in
addition to perform the same sinusoidal recordings with both
head-stages as we had done before, but without the additional
manipulations of the value of Z
a.
The results are shown in Fig. 6. The resulting normalized
gains (Fig. 6A) show that there was less voltage attenuation
in the physiological saline for both head-stages, though con-
siderable low frequency voltage drops still occurred with the

150 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
Fig. 6. Voltage attenuation, phase shifts and impedance measurements with
different saline concentrations. In all plots and colors, data recorded in physi-
ological saline is shown with dashed lines, and data recorded in dilute saline
is shown in solid lines. The saturation level of all colors reflects electrode
impedance, with the strongest colors showing data collected with the highest
impedance electrodes. The manufacturer specified 1 kHz impedance value for
each electrode is indicated in A. All electrodes were epoxylite-insulated. Blue
lines show data recorded with the low input impedance head-stage in the parallel
configuration, orange lines show data recorded with the high input impedance
head-stage in the parallel configuration, and green lines show impedance mea-
surements made with the Agilent LCR meter. Frequency is shown on a log scale
for all plots. For a list of the exact frequencies tested, please see Section 1.4.
(A) The normalized gain showing voltage attenuation across the electrode, as
in Fig. 3B and 4B. (B) The effective electrode impedance (Z
e) calculations,
derived from the low input impedance head-stage data only in A as well as
the measurements made by the Agilent LCR meter. A + denotes an electrode’s
manufacturer specified value at 1 kHz, and a ×denotes the value from the Bak
metal electrode impedance tester at 1 kHz made in dilute saline. Measurements
with the Bak tester in physiological saline were always somewhat lower than
the dilute saline values, but these are not shown for clarity. Z
eis shown on a log
scale. (C) Electrode-amplifier circuit-induced phase shifts.
low impedance head-stage for all tests performed. Interest-
ingly, at high frequencies some attenuation does consistently
occur for the high input impedance head-stage, and the gains
are similar to what is observed with the low input impedance
head-stage for the same electrodes and saline conditions. This
suggests that effects from shunt capacitance (Csh) in this record-
ing setup dominate the value of Z
aover this frequency range
and demonstrates that even when using a high input impedance
head-stage, investigators may want to take care to minimize this
capacitance to avoid minor to moderate spiking signal loss and
shape distortion. The electrode-amplifier circuit-induced phase
shifts for the same conditions are shown in Fig. 6C. This again
shows that the phase shifts co-occur with amplitude attenuation
which can both be quite large at low frequencies with the low
impedance head-stage in either saline concentration. This also
shows high frequency phase shifts that are largely independent of
the head-stage, as was found with the high frequency amplitude
effects.
Fig. 6B shows the resulting electrode impedances predicted
by the model based on the low impedance amplifier data in
addition to other corroborating measurements. As before, we
see that the impedance values resulting from the normalized
gains in dilute saline are consistently larger than the value
specified by the manufacturer. However, when performed in
physiological saline, we see that there is a decrease in impedance
measurements that is roughly two-fold across all frequencies.
This occurred in both the sinusoidal recordings and the mea-
surements of the Agilent LCR meter. The resulting impedance
measurements in physiological saline values match well with
the manufacturer specified impedances, suggesting the saline
concentration was the primary cause of the mismatch between
the manufacturer specified impedance values and our earlier
recordings.
It is important to note that this change in impedance across
different saline concentrations is not a result of the changed
resistance through the solution itself, but instead reflects
an effect on the impedance across the electrode/electrolyte
interface at the electrode tip. First, the data in each case is
compared to the steel pin reference electrode data recorded
under the same conditions to account for changes in the actual
voltage at the tip between conditions. The change in saline
concentration would however affect the value of Rsresulting
from the resistance encountered to reach the small electrode
tip. This has been estimated before to be largely negligible
in physiological saline compared to the impedance across the
electrode tip (Robinson, 1968). The dilute saline would be
expected to have a four-fold increase in resistivity compared
to physiological saline (Grimnes and Martinsen, 2000), but the
value of Rswould still remain largely negligible. Finally, the
value of Rswould not change with frequency. Since the absolute
impedance differences between saline concentrations are clearly
frequency-dependent, it further suggests that this results from
a change in the impedance across the electrode tip (Reand Ce).
2.5. Filter-induced phase shifts
Filters used in the data acquisition system (H(ω)) can cause
substantial phase shifts between Vin and Vrec that would add
to the phase shifts induced by the electrode-amplifier circuit.
To isolate this, we measured directly the phase of Vrec relative
to the phase of Vsig as a function of frequency for signals sent
directly to the head-stage (Vin =Vsig), shown in black (Fig. 7)
for the filters used in the rest of this study with both head-stages.
These phase shifts become large near the edges of the filters’
passbands, although the raw phase shift within the passbands of
these filters is considerable as well.

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 151
Fig. 7. Filter-induced phase shifts. The recorded phase shifts of signals sent
directly into head-stages used with different analog filters are shown, with spike
and LFP channel data overlapping. A positive phase means that the recorded
signal leads the actual signal. Frequency is shown on a log scale. For a list of
the exact frequencies tested, please see Section 1.4. Both head-stages were used
through-out this study with following preamplifiers with identical specified filter
properties, which had resulting phase shifts shown here in black. The data above
10 Hz were recorded using the low input impedance head-stage, and the data
at and below 10 Hz were recorded with the high input impedance head-stage
which has no series capacitance that introduces additional phase shifts in this
frequency band (see Fig. 10). This black line was used as the purely filter-induced
reference phase and subtracted from other data recorded with this equipment to
determine the phase shifts introduced by other sources. The grey line shows the
LFP channel phase shifts recorded for a second preamplifier with the high input
impedance head-stage. The dotted vertical lines show the cut-off frequencies for
the LFP channel filter with its phase response shown in the corresponding color.
Fig. 7 shows another characteristic of filter-induced phase
shifts. Over the narrow frequency range where a given signal
can be recorded simultaneously through both the spike and the
LFP channels, the outputs of the two channels are out of phase
with each other. While expected, this result clearly demonstrates
that different phase shifts arise from the different filter properties
of the two channels. To further illustrate this, we used a second
LFP preamplifier with different filter properties to record sig-
nals up to 300 Hz, with results shown in grey in Fig. 7.Even
in the region where the passbands of the two LFP amplifiers
overlap, considerable differences in the phase response occur,
with each LFP preamplifier inducing characteristic shifts from
the phase of the input signal. We have also found that phase
shifts near the filter passband edges can vary from channel to
channel for a given preamplifier (Figure S2, see Supplementary
results online). Thus, equipment-specific filtering properties
must be accounted for to report accurately the phase of LFP
data, especially at frequencies near the passband edges of analog
filters.
2.6. Group delay
The phase shift at a given frequency can be translated into
a time delay for a pure sinusoid at that frequency. If the phase
shifts were constant across frequencies, this would correspond to
a progressively decreasing time shift as the frequency increases.
On the other hand, if the phase shifts of a system were the result
of a pure time delay of the signal, then the phase response would
be a linear function of frequency, with the magnitude of the slope
reflecting the magnitude of the delay. The negative derivative of
the phase with respect to frequency, called the group delay, is a
useful measure of delay even when the phase response is non-
linear. For a narrow bandwidth around a given frequency where
the variation of phase with frequency is approximately linear,
the group delay measures the delay of the amplitude envelope
for all components of signals within this narrowband “group” of
sinusoids (Oppenheim and Schafer, 1998; Smith, 2006). Note
that at any particular frequency, the group delay need not equal
the time shift calculated directly from the phase shift (i.e., the
phase shift in fractions of a cycle divided by the frequency),
which is called the phase delay. The two delays will differ over
at least some part of the spectrum if the system’s phase response
is not entirely linear. When the group delay and phase delay
are not equal, the system will necessarily distort the shapes of
signals in the time domain (Smith, 2006).
Fig. 8A shows the group delay for the electrode data; this is
just the negative derivative of the low input impedance head-
stage phase data from Fig. 5 (in units of cycles) with respect
to frequency (see Eq. (4), Section 1) without the subtraction
of the filter-induced reference phase. Group delay varies mod-
estly with electrode impedance and generally decreases with
increasing frequency. For comparison, the group delay calcu-
lated from the filter-induced phase shifts of the black line in Fig. 7
is shown here, and the group delay for the metallic resistor data
is shown in Fig. 8B. The filter-induced group delay through the
LFP channel is relatively constant from 25 to 85 Hz at ∼3 ms, and
the group delay through the spike channel above 1 kHz is con-
stant at ∼0.15 ms. The electrode-amplifier circuit-induced phase
shifts in the microelectrode data resulted in added delays in the
LFP frequency range that varied on average from an additional
0.35 ms at 85 Hz to 1.10 ms at 35 Hz. Over lower frequencies, the
additional delays were even larger for some electrodes, with the
series capacitance within the low impedance head-stage partly
contributing to this. Recall that the purely filter-induced group
delays from either head-stage will be the same as both use the
same filters with the same phase response. To summarize, the
group delay in the spike-related frequency range will not distort
spike timing appreciably, but the group delay in the LFP fre-
quency range will introduce a systematic delay that can become
quite large at lower frequencies.
These conclusions depend on the quality of the group delay
function derived from the phase shift measurements. To obtain
a more direct measurement of group delay, we sent narrowband
filtered pulses (see Section 1for description, Fig. 9 for exam-
ples) and measured the time delay at which the cross-correlation
between the actual and recorded envelope estimates was maxi-
mal. The dotted traces in Fig. 8A show the results for two of the
electrodes color-coded for the electrode’s impedance. Each of
these traces matches very well the electrode’s calculated group
delay. Other electrodes tested in this manner also showed good
matches with their group delays, as did the metallic resistor data
(Fig. 8B). This confirms that the group delay measured for this
system actually measures the delay of the amplitude envelope
of a signal at a given frequency, which differs from the phase
delay of the signal directly calculated from the phase shift of the
carrier frequency.

152 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
Fig. 8. Group delays. Spike and LFP channel data are shown overlapping. Fre-
quency is shown on a log scale. For a list of the exact frequencies tested, please
see Section 1.4. The filter-induced phase shifts were not subtracted from any
data shown here. (A) Group delay for electrode data. Grey-to-blue lines show
data recorded in dilute saline in the parallel configuration using the low input
impedance head-stage for electrodes with low-to-high measured impedance val-
ues at 10 Hz. Solid lines show group delays calculated from Eq. (4) (see Section
1) using the recorded phase shifts of sine waves at different frequencies, while
dotted lines show the measured amplitude envelope delay using narrowband
filtered pulse signals recorded with two electrodes. The manufacturer specified
values at 1 kHz are indicated in the color legend above the plot. Values in italics
and followed by an asterisk denote data from a glass-insulated electrode. The
group delays from the filter-induced reference phase response (the black lines
from Fig. 8) are shown by the black line for comparison. (B) Group delay for
metallic resistor data. Line colors are coded from grey to red based on the value
of Rm, with the precise values for each line indicated above the plot. The dot-
ted black line shows the measured amplitude envelope delay using narrowband
filtered pulse signals sent directly to the head-stage with no resistors, which
corresponds well with the calculated group delay. The dotted vertical lines show
the cut-off frequencies for the LFP channel filter used.
2.7. Distortion of field potential and spike waveforms
Because the group delay and phase delay are not equal over
many frequencies, and because of the amplitude attenuation by
analog filters and the electrode itself, we expect distortion of
recorded waveform shapes in the time domain to occur. To view
this, we recorded with and without microelectrodes a voltage
shape obtained from a single neuron’s recorded waveform as
well as a frequency-modulated version of the same waveform
Fig. 9. Examples of filtered frequency pulses used for amplitude envelope and
group delay measurements. Actual signals presented directly to the head-stage
are shown in green, recorded signals are shown in red. For each signal, the raw
values are shown with solid lines and the Hilbert-magnitude estimations of the
amplitude envelope with local average smoothing applied are shown with dotted
lines. The maximum point of each estimated envelope is shown with vertical
dashed lines. Data are presented for bandpass filtered pulses centered around
frequencies of (A) 1 Hz, (B) 50Hz and (C) 1 kHz. LFP channel data are shown
in A and B, spike channel are data shown in C.

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 153
Fig. 10. Recorded waveform shapes. Grey-to-blue lines show waveforms recorded in the parallel configuration in the low input impedance head-stage for electrodes
with low-to-high measured impedance values at 10Hz. The manufacturer specified value at 1kHz indicated in the color legend above the plot. Values in italics and
followed by an asterisk denote data from a glass-insulated electrode. The thin grey line shows the actual voltage presented, and the thick black line shows the voltage
recorded with the signal voltage applied directly to the same head-stage. Dilute saline was used for the electrode recordings in A and B, and physiological saline was
used for the data in C and D. (A) LFP channel data only for a lower-frequency version of the waveform. (B) Spike channel data only for a higher-frequency version
of the waveform. Beneath each plot is a power-spectral density (PSD) estimation of the actual voltage waveform in each plot, obtained with a windowed Fourier
transform. (C) and (D): 10 and 80 Hz frequency pulse waveforms additively combined with the high frequency spike from B. LFP channel data is displayed with the
Spike channel data additively combined to it at the time of the recorded spike.
with the signal power concentrated in the LFP frequency ranges
(Fig. 10). Fig. 10A shows the results for the LFP frequency
range waveform, in which the delay in the recorded signal of
about 3–4 ms can be clearly seen, matching the group delay for
the relevant frequency ranges comprising this waveform. Elec-
trode impedance-dependent distortion of the recorded shapes
can also clearly be seen, probably resulting largely from the
amplitude attenuation properties of the electrode, with more of
the lower frequencies of the signal being filtered out as electrode
impedance increases.
Fig. 10B shows the results for the raw waveform in the spike
frequency range, in which the shorter (∼0.1 ms) delay can also
clearly be seen. The effect of electrode impedance can be seen
in the progressive attenuation of the amplitude of the recorded
waveform, with a tendency for both the electrode and non-
electrode data to attenuate the first large negative trough more
so than the following large positive peak. The most conspicuous
shape distortion though, is the phantom after-hyperpolarization
that is not present in the input signal. Of course the sub-ms
delay in the overall timing of the spike will have little apprecia-
ble impact since the precision of spike timing is rarely important
to that degree. However, the amplitude attenuation of the spikes
could potentially make it more difficult to record and isolate
spikes among noise, particularly with higher impedance elec-
trodes. As we showed earlier, this cannot be avoided with higher
impedance amplifiers since Z
ain this frequency range is dom-
inated by the shunt capacitance, at least for our experimental
setup. The filter-induced phantom after-hyperpolarization sug-
gests that any inferences made about this portion of the action
potential in particular without adjusting for the distortion would
be misleading.
Finally, to demonstrate the effects of these distortions on
simultaneously recorded spikes and LFPs, we used frequency
pulses with the high frequency spike from Fig. 10B added to the
signal at the maximum of the highest central peak. The results
from one medium impedance electrode in physiological saline
using either head-stage are shown in Fig. 10C and D. For the
10 Hz signal, the filter-induced phase shift happens to be near
zero at this frequency (see Fig. 8), resulting in a near-zero phase
shift observed with the high impedance head-stage. However,

154 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
electrode-amplifier circuit-induced phase shifts with the low
impedance amplifier cause the carrier wave of the recorded sig-
nal to lead the actual signal causing the recorded spike to appear
on the falling edge of the recorded LFP oscillation instead of at
its true position at the peak. For the 80-Hz signal, the direction of
the filter-induced and electrode-amplifier circuit-induced phase
shifts counteract each other, with the filter-induced phase shifts
dominating and causing the recorded spike to appear well on
the rising edge of the recorded LFP oscillation instead of at its
true position at the peak. It is worth noting that this considerable
filter-induced phase shift occurs at this frequency even though
based solely on the high frequency cut-off of 170 Hz one might
superficially expect the phase shift to be negligible at 80 Hz.
3. Discussion
3.1. Summary
We have shown that signals recorded with tungsten micro-
electrodes and an acquisition system commonly used in
neurophysiology can be distorted substantially from the actual
signals at the electrode tip. This distortion consists of frequency-
dependent phase shifts and amplitude attenuation. The system
filters imposed noticeable phase shifts even within their pass-
bands. The observed phase shifts were dependent on the exact
specifications of the preamplifier selected for use in a given sys-
tem. When the electrode impedance was high with respect to
the effective input impedance of the head-stage amplifier, both
attenuation and additional phase shifts of the recorded signal
occurred. Of the two head-stages we tested, this occurred with
the lower input impedance head-stage and primarily at lower
frequencies because of the oft-overlooked fact that microelec-
trode impedance becomes much higher as frequency decreases.
As such, equipment designed primarily to record spiking activ-
ity may not be able to record LFP activity without distorting
the signal. We demonstrated that the distortions decrease with
increasing saline concentration, but are still considerable with
the low input impedance head-stage in physiological saline.
Thus, these effects are of particular importance when gathering
and interpreting LFP data. We showed that phase effects from
both sources lead to amplitude envelope delays that differ from
the direct time equivalent of the phase shift at a given frequency.
We have also demonstrated shape distortion effects on recorded
lower frequency event-triggered potentials and spike shapes.
3.2. Impact of distortions
If the distortions demonstrated in this study occur and are not
accounted for, any analysis using such LFP or spike shape data
would be affected, and in certain cases this may lead to incorrect
conclusions. Negative results at lower frequencies in LFP power
or coherence (Fries et al., 2001a; Liu and Newsome, 2006), par-
ticularly at sub-gamma frequencies (<40 Hz) become difficult to
interpret as are direct comparisons of these measures across fre-
quencies (Fries et al., 2001b; Rickert et al., 2005; Womelsdorf et
al., 2006). Measures of absolute LFP phase in relation to an event
or spikes will be shifted (Bragin et al., 1995; Haslinger et al.,
2006; Lee et al., 2005; Lin et al., 2006; Murthy and Fetz, 1996;
Skaggs et al., 1996) meaning that any mappings of potentials
onto the times when neurons locally are excited and inhibited
(Fries et al., 2001a; Haslinger et al., 2006; Lin et al., 2006) will be
incorrect. Because of the amplitude envelope delays, there will
be subtle delays imposed on the timing of changes in frequency
power or coherence (Womelsdorf et al., 2006). And finally, the-
oretical interpretations of spike shapes (Barth´
o et al., 2004; Gold
et al., 2006; Mitchell et al., 2007; Nowak et al., 2003) and event-
triggered LFPs (Fries et al., 2001a,b; Kreiman et al., 2006) may
be incorrect, and techniques using waveforms as classification
data (Fries et al., 2001a; Kreiman et al., 2006) will be affected
as well.
We would like to clearly indicate that we are not claiming
that the results of any of the articles we mention above are
necessarily distorted or that all of their conclusions should be
questioned even if some signal distortion did occur. Indeed dif-
ferent equipment than what we have tested was often used, and
such studies may or may not be susceptible to such distortions
to a similar degree. However, due to past and current standards
in the literature regarding methodological documentation it is
not possible for a reader to determine the extent to which LFP
data in a given publication may have been affected or to be cer-
tain that such distortions are negligible. In a qualitative review
of the LFP literature, we found that though cut-off frequen-
cies for filter passbands are usually mentioned, the filter phase
response is rarely mentioned. The filter specifications that are
given are typically insufficient for the reader to be sure that the
phase response will be near zero for the frequency ranges in
question, even in cases where this would affect some of the con-
clusions of the article. Electrode impedance ranges measured at
1 kHz are only occasionally mentioned. The names of compa-
nies providing the amplification and recording equipment are
also occasionally mentioned, but importantly, specific model
numbers or relevant input impedances of amplifiers are never
mentioned. This additional information should be included as
well, as we have shown that different products provided by the
same company can be susceptible to different levels of distor-
tions. Indication of accounting for all the signal distortions we
have shown is also never given.
Additionally, though some conclusions from analyses we
have mentioned may be rendered incorrect as result of distor-
tions that were not considered, this will not be true of conclusions
from all analyses of such data. Most notably, comparisons within
a given frequency band across different conditions using the
same equipment should remain valid, though such comparisons
at lower frequencies may be subject to a lower signal to noise
ratio. While it is possible that rigorous statistical testing like
bootstrapping and other methods could alleviate this to a certain
extent, if potential distortions are a problem for a given data
set, uncertainty regarding negative results at low frequencies
would inevitably remain regardless of the statistical procedures
employed on the distorted data. If the signal is analyzed in the
time domain which combines LFP activity from all frequencies,
then if the underlying neural activity between the two condi-
tions differs at all then their frequency content must differ and
the distortions will affect the recorded activity under each condi-

M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157 155
tion differently. As we have shown, the time domain waveform
shape of the signal can be distorted, which would thus affect
such comparisons across conditions, most notably for results
involving the precise timing of activity.
However, an impact of unaccounted signal distortion that is
much more important than whether or not it may render a given
specific analysis to be strictly wrong is that it leads to an overall
distorted view of the underlying neural activity and the state of
the brain during experiments. With LFPs in particular, though
some progress can be made using recorded activity merely as an
arbitrary signal with which to determine when activity in a brain
area generally differs between conditions, of critical importance
to truly understanding the brain will be to determine what the
underlying brain states are that give rise to the recorded neural
activity. Signal distortions that are not accounted for will lead
such mappings to be incorrect. For example, in one recent study
(Lin et al., 2006) the authors note that basal forebrain tonic
neurons (BFTNs) synchronize spiking activity just before the
troughs of recorded prefrontal cortex (PFC) LFP theta oscilla-
tions of about 10 Hz. They interpret this as suggesting that the
BFTN synchronization leads and probably contributes to a cor-
tical activity increase that results in the LFP trough. Inferences
like these are potentially the most fruitful uses of LFP activ-
ity to improve our understanding of the brain. However, if their
recordings were distorted, which a reader cannot ascertain, then
their general finding that BFTN synchronization occurs phase
locked with PFC theta activity would likely still be true, but the
reported phase at which this occurs and the theoretical interpre-
tation of this relative to the timing of cortical excitation may
need to be adjusted.
Because the distortions we have shown can implicate differ-
ent underlying neural activity as giving rise to recorded data and
can also potentially alter certain direct conclusions, they should
be kept in mind when interpreting any LFP result, though we
cannot quantify their extent in any given existing article. Our
results also emphasize the importance of including methodolog-
ical details in publications. Of course not every trivial detail of
an experiment can be mentioned so a proper balance must be
found, but our work illustrates some of the problems that can
result from reporting too little. In particular, the mindset that a
reader should assume that methodological details not mentioned
in the article were done correctly by the experimenters without
any verification of that has obvious negative consequences for
the advancement of science. Particularly with the advent of web-
based supplementary materials there is ample room to put full
details of the experimental apparatus in publications. We also
encourage instrument providers to post more complete informa-
tion on their web sites. However, we feel it is most appropriate
for the specific equipment used in a study to be documented in
the article text or Supplementary information, rather than solely
in an external source like a lab website. This avoids confusion as
the equipment used often varies between projects in a lab and it
allows the reader to more easily find the information they need.
While we hope that our results will lead readers to view
existing LFP literature in a somewhat different light, our pri-
mary concern is that those performing future neurophysiology
experiments will be more aware of these distortions and either
avoid them entirely or account for them properly. Additionally,
it is important for authors themselves to understand how this
recording circuit works, which reveals in what instances and in
what ways electrode characteristics like impedance will affect
recorded signals. Investigators should not solely rely on equip-
ment providers to ensure that their recordings are done correctly.
Among other reasons, the way that equipment is arranged in a
particular experiment independently of how it is built affects the
shunt capacitance. We have shown that even with the best of
equipment, this could lead to degradation of recorded spiking
activity, making isolating single cell activity in the brain more
difficult.
With regards to electrode-amplifier circuit-induced distor-
tions, while our results indicate that this will be a problem for
a low impedance head-stage that has been in use by some for
recording LFPs, this is not true of all available amplifiers as we
have demonstrated with a higher impedance head-stage. Indeed,
amplifiers with very high input impedances have been easily
obtainable for some time (Purves, 1981). It cannot be our place
to test all the equipment used in neurophysiology today, but we
hope that in light of what we have shown, prudent labs will deter-
mine what distortions arise in their experiments, particularly
if their work involves recording LFPs. We cannot say exactly
how widely used the 38 Mhead-stage that we tested in this
study is, but we do know that some other labs have been using it
for recording LFPs with microelectrodes. Additionally, it seems
likely to us that other equipment providers may have addition-
ally distributed equipment that results in at least some degree of
low-frequency signal distortion, as problems could easily result
from overlooking or being unaware of the large increases in
electrode impedance at low frequencies. Considering electrode
impedances at 1 kHz as they are often labeled, amplifier input
impedances of several tens of Measily seem sufficiently high,
though we have shown that indeed they are not for the recording
of LFPs.
With regards to filter-induced distortions, provided that ana-
log filters are used before digitizing and recording potentials,
which is for all practical purposes a requirement for most record-
ing systems, phase distortions will necessarily occur as they are
a property of any causal filter. These distortions are therefore far
more prevalent, though they are seldom accounted for in exist-
ing LFP studies. Sensitivity to this issue should also be present
when considering the use of post-recording digital filters, as
many of these may introduce phase shifts as well but carefully
implemented ones may not. Potential filter-induced phase shifts
should always be kept in mind when interpreting existing and
future results reporting the absolute phases of field potentials
(Bragin et al., 1995; Haslinger et al., 2006; Lee et al., 2005; Lin
et al., 2006; Murthy and Fetz, 1996; Skaggs et al., 1996), shapes
of spikes (Barth´
o et al., 2004; Gold et al., 2006; Mitchell et al.,
2007; Nowak et al., 2003) and evoked potentials (Fries et al.,
2001a,b; Kreiman et al., 2006).
3.3. Correction techniques
An easy way to avoid the electrode-amplifier circuit-induced
portion of the effects that we have shown is through hardware

156 M.J. Nelson et al. / Journal of Neuroscience Methods 169 (2008) 141–157
adjustments with the use of a head-stage with a much higher
input impedance than the 38-Mhead-stage tested for most of
this study. As we have shown, amplifiers with low frequency
input impedances of 1 Gare sufficient to eliminate this dis-
tortion for all practical purposes with the use of most metal
microelectrodes under reasonable conditions. It should also be
noted that shunt capacitance can compromise even the high-
est amplifier input impedances, so care must always be taken
to minimize this, for example with the use of minimal-length
cables between the electrode and head-stage, negative capaci-
tance injection, driven shield arrangements or other techniques
(Purves, 1981, pp. 45–49).
Care should also be taken to select filter properties appro-
priate for the intended analyses, another useful hardware
adjustment. Passband edges should be placed as far off as pos-
sible from the frequency ranges of interest since the region of
negligible phase shift is somewhat narrower than the region of
negligible amplitude attenuation. The number of poles and type
of filter can be selected to achieve the proper balance between
phase distortions and amplitude response fluctuations in the
passband, both of which form tradeoffs with each other.
For any of the effects we have shown that could not be avoided
during data acquisition, software adjustments involving ex post
facto correction routines using de-convolutions are possible to
account for them once the transfer function of all the elements
in the circuit are known. This is easily obtainable for the record-
ing system itself by recording sine wave voltages spanning the
frequency spectrum of interest with a desired resolution as we
have done in this study, though other techniques like the use of a
chirp signal may be possible, which would only require the use
of one test signal. Signals can be generated using a function gen-
erator or a computer’s audio output as was done in this study. If
additional electrode-amplifier circuit-induced effects could not
be sufficiently mitigated with an appropriate head-stage, mea-
surements of the system transfer function including the electrode
would need to be performed as well. Preferably, this should be
done within the brain before and after a recording session to
get the best estimate of the transfer function resulting from the
electrode’s impedance at the time of recording. Available online
in the Supplementary materials is a text file containing Mat-
lab code to generate .wav files for signal generation, interpret
the recorded data to obtain the transfer function, and apply the
correction techniques given the empirically obtained transfer
function. For Plexon users, a software tool provided by Plexon
for correcting preamplifier phase distortions can be downloaded
from http://www.plexoninc.com/support/phase.html.
3.4. Other electrode variables
There is no indication that the nature of the equivalent circuit
described in this article will depend on electrode characteris-
tics, though the value of specific model parameters may. For
example, insulation material may affect the shunt capacitance
to ground, as glass insulation for example has been known to
be more capacitive than epoxylite (Robinson, 1968), but with
recordings at a negligible depth we found that results with dif-
ferent insulation materials were not qualitatively different. The
physical properties of an electrode, which we have not inves-
tigated here, may also considerably affect the signals recorded
by an electrode in a complicated physical environment like the
brain (Lemon, 1984).
The basic equivalent circuit we present applies to other types
of microelectrodes as well, including glass micropipette, car-
bon fiber and microwire electrodes. These typically have much
higher impedances than metal microelectrodes and it has been
suggested that with such electrodes experimenters have typically
used appropriately high input impedance amplifiers (Geddes et
al., 1967), though we feel documentation of this is still warranted
in articles presenting such data.
Disclosure statement
The authors affiliated with Vanderbilt University have no
competing interests. The authors associated with Plexon have
competing interests.
Acknowledgements
We would like to thank Justin Crouse at FHC for valuable dis-
cussions, Bruce Williams for construction of and assistance with
the design of the electrode testing apparatus, and AB Bonds for
valuable discussions and comments regarding the manuscript.
Grants: This work was supported by RO1-EY08890, Robin
and Richard Patton through the E. Bronson Ingram Chair of Neu-
roscience and center grants P30-EY08126 and P30-HD015052.
Appendix A. Supplementary data
Supplementary data associated with this article can be found,
in the online version, at doi:10.1016/j.jneumeth.2007.12.010.
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