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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.

Figure 1:

Figure 2:

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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