At low
frequencies parasitic capacitance can usually be ignored, but in high frequency circuits it can be a major problem. In
amplifier circuits with extended frequency response, parasitic capacitance between the output and the input can act as a
feedback path, causing the circuit to
oscillate at high frequency. These unwanted oscillations are called
parasitic oscillations. In high frequency amplifiers, parasitic capacitance can combine with stray inductance such as component leads to form
resonant circuits, also leading to parasitic oscillations. In all inductors, the parasitic capacitance will resonate with the inductance at some high frequency to make the inductor
self-resonant; this is called the
self-resonant frequency. Above this frequency, the inductor actually has
capacitive reactance. The capacitance of the load circuit attached to the output of
op amps can reduce their
bandwidth. High-frequency circuits require special design techniques such as careful separation of wires and components, guard rings,
ground planes,
power planes,
shielding between input and output,
termination of lines, and
striplines to minimize the effects of unwanted capacitance. In closely spaced cables and
computer busses, parasitic capacitive coupling can cause
crosstalk, which means the signal from one circuit bleeds into another, causing interference and unreliable operation.
Electronic design automation computer programs, which are used to design commercial
printed circuit boards, can calculate the parasitic capacitance and other parasitic effects of both components and circuit board traces, and include them in simulations of circuit operation. This is called
parasitic extraction.
Miller capacitance causes a feedback impedance Z between the input and output of an amplifier to apparently be multiplied by a little more than the amplifier's gain A_v when viewed as an input impedance Z_{in}. Parasitic capacitance in an inverting
amplifier component like a
transistor is especially problematic because it is multiplied by the gain of the amplifier due to the
Miller effect. Assume the ideal inverting amplifier with
gain of A_\nu in Figure 2 has a parasitic capacitance between the amplifier's input and output as the feedback impedance (Z{=}C_\text{parasitic}). If the amplifier itself has infinite
input impedance, the current from the input terminal through Z is: :i_\text{Z} = C_\text{parasitic} \, {d \over dt}(V_\text{i} - V_\text{o}) \, :i_\text{Z} = C_\text{parasitic} \, {d \over dt}(V_\text{i} + A_\nu \, V_\text{i}) \, :i_\text{Z} = \underbrace{(1 + A_\nu) \, C_\text{parasitic}}_{C_\text{Miller}} \, {dV_\text{i} \over dt} \, . Even a small parasitic capacitance is problematic because the
Miller effect multiplies it by 1 + A_\nu (or approximately A_\nu for amplifiers with high gain) when viewed as an input capacitance C_\text{Miller}.
Impact on frequency response If the input circuit has an impedance to ground of R_i, then (assuming no other amplifier poles) the output of the amplifier is :V_\text{o} = \frac{A_\nu}{1 + j\omega R_\text{i}C_\text{Miller} }V_\text{i} \, , which depends on the
angular frequency \omega = 2 \pi f. This acts as a
low-pass filter with a
cutoff frequency that limits the amplifier's
bandwidth to: :f_\text{cutoff} = {1 \over 2\pi R_\text{i}C_\text{Miller}} = {1 \over 2\pi R_\text{i}C_\text{parasitic} \, (1 + A_\nu)} \, . The voltage gain of modern transistors can be 10–100 or even higher, and for
op amps are orders of magnitudes higher, so
Miller capacitance (first noted in
vacuum tubes by
John Milton Miller in 1920) is a significant limitation on the high frequency performance of amplifying devices. The
screen grid was added to
triode vacuum tubes in the 1920s to reduce parasitic capacitance between the
control grid and the
plate, creating the
tetrode, which resulted in a great increase in operating frequency. In
bipolar junction transistors, the parasitic capacitances between the base and collector or emitter have voltage dependence too. ==See also==