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Miller Capacitance Effects and Cin Analysis
The Miller effect is the apparent modification of capacitance effects by a factor of the voltage
gain between the capacitor terminals. In Figure 1, the signal Vin will appear at Vo ,
VGS , Vin , AGD = -gmZL , larger and inverted.
The signal Vin will also appear as Vs , AGSVin and in phase with
the input (AGS is the source follower gain from gate to source).
AGS: RS / RS + 1/gm
The circuit obviously has Gain from the input (gate) to drain and from the input (gate) to source.
The Miller effect must be expected to cause the capacitors CGD and CGS to
have effects, do to the gain across their terminals, that is modified by the gain.
To simplify the analysis, examine the Miller effect relative to CGD by examining a grounded
source circuit (Figure 2). For this circuit, the input capacitance will be CGS plus CGD
as modified by the Miller effect. Examine the equivalent circuit of Figure 2, shown in Figure 3.
Figure 3:
Analyze the circuit for Zin which, as shown, will result in the "Z" of the total capacitance
Cin. From this it will be possible to determine the Miller Effect on CGD.
Zin = Vin / iin → iin + iGD - iGS = 0 →
iGS = Vin / (1/jωCGS)
iGS = jωCGSVin
iGD = (Vo - Vin) / (1/jωCGD)
iGD = (Vo - Vin)( jωCGD)
Vo = AVin, {where A = -gmZL}
iGD = (AVin - Vin) jωCGD →
iGD = Vin(A - 1) jωCGD
iGS = Vin(jωCGS)
iin = iGS - iGD → iin = Vin(CGS +
CGD(1 - A)) jω
So: Zin = Vin / iin = Vin / Vin(CGS +
CGD(1 - A)) jω
However, Zin is also the reactance (impedance) of Cin, the total input capacitance
made up of CGS and CGD modified by the Miller effect.
Zin = 1 / jωC = 1 / (CGS + CGD(1 - A)) jω
∴ Cin = CGS + CGD(1 - A)
for the grounded source amp (A = -gmZL)
In the amp with an unbypassed source resistor: Cin = CGS(1 - AGS) +
CGD(1 - AGD)
Engineering key words: Miller effect, miller affect, capacitance, cap, drain, gate, source, FET,
JFET, BJT, input gain, leakage current, amplifier, circuit analysis, ground, admittance, resistive,
operating frequency, total, impedance, inductive, phase.
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