Measurement of effective amplifier input impedance. Plots show amplitude data from signals sent directly to the low input impedance head-stage across different metallic resistors (R_m). Line colors are coded from grey to red based on the magnitude of R_m, with the precise values for each line indicated in A. Spike and LFP channel data (see Methods) 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 the Signals used subsection in the Methods section. 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 R_m was 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.

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 10 Hz. 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 8.4 MΩ. Parallel configuration data is shown with solid lines, series configuration data is shown with dashed lines. A and B denote parallel confugration recordings with no Z_a’ manipulations, and C shows the average parallel and series configuration values across 4 different values of Z_a’. Spike and LFP channel data (see Methods) 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 the Signals used subsection in the Methods section. A: raw gain of the recorded over the actual signal. B normalized gain showing 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_e’ is shown on a log scale.

Voltage attenuation, phase shifts and impedance measurements with different saline concentrations. In all plots and colors, data recorded in physiological 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 measurements 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 the Signals used subsection in the Methods section. A: the normalized gain showing voltage attenuation across the electrode, as in figures 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 x 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_e’ is shown on a log scale. C: electrode-amplifier circuit induced phase shifts.

Group delays. Spike and LFP channel data are shown overlapping. Frequency is shown on a log scale. For a list of the exact frequencies tested, please see the Signals used subsection in the Methods section. 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 values at 10 Hz. Solid lines show group delays calculated from equation 4 (see methods) 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 Figure 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 R_m, with the precise values for each line indicated above the plot. The dotted 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.

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 10 Hz. 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.

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 (R_s), the resistance and capacitance at the double layer interface of the electrolyte and the uninsulated electrode tip (R_e and C_e) and the (negligible) resistance of the metal electrode (R_m). The effective input impedance of the amplifier (Z_a’) is comprised of the input impedance of the head-stage amplifier (Z_a) and the shunt resistance and capacitance to ground from the tip of the electrode to the input of the amplifier (R_sh and C_sh). The triangle represents an ideal amplifier that draws no current. The non-ideal aspects of the amplifier have been accounted for in Z_a. Given the frequency-dependent potential at the electrode tip (V_sig(ω)), a current (I(w)) is drawn towards ground through the electrode and effective amplifier circuit, creating the potential (V_in(ω)) at the input of the amplifier which is subject to the frequency response of analog filters (H(w)) before being recorded (V_rec(ω)), all according to the equation: V_rec(ω) = H(ω)[(V_sig(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 dependence of the impedances Z_e’ and 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 apparatus was immersed in dilute saline with voltage signals applied to the signal plate with an electrode suspended from above 3 mm away. See the Methods section for more details. C: equivalent circuits for the parallel and series configuration. R_sal1 is the resistance for current to travel from the signal plate to the electrode tip in the saline, and R_sal2 is the remaining resistance for current to reach the ground plate.

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_a’ with the low input impedance head-stage. Line colors are coded from grey to blue based on the value of Z_a’ at 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 Methods) 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 the Signals used subsection in the Methods section. 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_e’ is shown on a log scale.

Electrode-amplifier circuit induced phase shifts using electrodes. All phase shifts are shown after subtracting the phase shifts induced by the system filters (see Figure 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 the Signals used subsection in the Methods section. 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 10 Hz. 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_a’ at 10 Hz, with the precise values indicated.

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 the Signals used subsection in the Methods section. 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 Figure 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.

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: 50 Hz, and C: 1kHz. LFP channel data are shown in A and B, spike channel are data shown in C.