hardware//electronics//impedance
Impedance says how much a part of a circuit opposes a signal that changes in time, and it is the number an engineer checks to know whether a small signal will survive the trip from a sensor into an amplifier. It generalises resistance: resistance is the opposition to a steady current, \(R = V/I\), and impedance \(Z\) is the same ratio for a signal that varies, which depends on how fast it varies, \(Z = Z(f)\).
Impedance says how much a part of a circuit opposes a signal that changes in time, and it is the number an engineer checks to know whether a small signal will survive the trip from a sensor into an amplifier. It generalises resistance: resistance is the opposition to a steady current, R=V/IR = V/IR=V/I, and impedance ZZZ is the same ratio for a signal that varies, which depends on how fast it varies, Z=Z(f)Z = Z(f)Z=Z(f).
The dependence on frequency comes from parts that store energy. A capacitor lets a fast signal through more easily than a slow one, and an ideal one has
∣ZC∣=12πfC|Z_C| = \frac{1}{2\pi f C}∣ZC∣=2πfC1
so a larger capacitance CCC or a higher frequency fff means a lower impedance, and at zero frequency (direct current) it blocks completely. A resistor has the same impedance at every frequency, and real parts combine both.
Impedance is resistance for signals that move.
A sensor with a high impedance loses part of its signal before the amplifier and adds noise of its own, so the first rule of any front end for faint signals is a low source impedance.
Source and load share the signal as a divider. A sensor of impedance ZsZ_sZs feeding an amplifier of input impedance ZinZ_{in}Zin delivers Vin=Vs Zin/(Zs+Zin)V_{in} = V_s,Z_{in}/(Z_s + Z_{in})Vin=VsZin/(Zs+Zin), so the amplifier needs an input impedance far larger than the sensor's or it reads only a fraction of the signal.
A resistive impedance makes noise. Thermal agitation of the charges in any resistance produces a noise voltage vn=4kTR Δfv_n = \sqrt{4kTR,\Delta f}vn=4kTRΔf, which grows with the root of the resistance and of the bandwidth Δf\Delta fΔf; for signals of microvolts that floor decides what can be measured.
An electrode in a liquid is mostly a capacitor. At the boundary between a metal and a salt solution the ions and electrons form a thin double layer that behaves capacitively, so electrodes are compared by their impedance at a stated frequency (1 kHz by convention), and a rough coating that multiplies the real surface lowers it. Low impedance is an electrical property; whether the tissue tolerates the electrode is a separate question.
The signal leaves the analog world at the analog-to-digital converter, which is why the impedance of everything before it matters most.