Miller Effect Capacitance

• Any P-N junction can develop capacitance. This was mentioned in the chapter on
diodes.
• In a BJT amplifier this capacitance becomes noticeable between: the Base-
Collector junction at high frequencies in CE BJT amplifier configurations.
• It is called the Miller Capacitance.

• It effects the input and output circuits.
• Ii = I1 + I2 Eqn (1)
• Using Ohm’s law yields
I1 = Vi / Zi,
I1 = Vi / R1
and I2 = (Vi – Vo) / Xcf
= ( Vi – AvVi) / Xcf
I2 = Vi(1 – Av) / Xcf
Substituting for Ii, I1 and I2 in eqn(1),
Vi / Zi = Vi / Ri + [(1 – Av)Vi] /Xcf
1/ Zi = 1/Ri + [(1 – Av)] /Xcf
1/ Zi = 1/Ri + 1/ [Xcf / (1 – Av)]
1/ Zi = 1/Ri + 1/ XCM
Where, XCM = [Xcf / (1 – Av)]
= 1/[w (1 – Av) Cf]
CMi = (1 – Av) Cf
CMi is the Miller effect capacitance.
• For any inverting amplifier, the input capacitance will be increased by a Miller
effect capacitance sensitive to the gain of the amplifier and the inter-electrode
( parasitic) capacitance between the input and output terminals of the active
device.
Miller Output Capacitance (CMo)
Applying KCL at the output node results in:
Io = I1+I2
I1 = Vo/Ro
and I2 = (Vo – Vi) / XCf
The resistance Ro is usually sufficiently large to permit ignoring the first term of the
equation, thus
Io @ (Vo – Vi) / XCf
Substituting Vi = Vo / AV,
Io = (Vo – Vo/Av) / XCf
= Vo ( 1 – 1/AV) / XCf
Io / Vo = (1 – 1/AV) / XCf
Vo / Io = XCf / (1 – 1/AV)
= 1 / wCf (1 – 1/AV)
= 1/ wCMo
CMo = ( 1 – 1/AV)Cf
CMo @ Cf [ |AV| >>1]
If the gain (Av) is considerably greater than 1:
CMo @ Cf

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