# Parasitic Capacitance

Parasitic capacitance , or stray capacitance , is an unavoidable and usually unwanted capacitance that exists between parts of an electronic component or circuit because of their proximity to one another. When two electrical conductors at different voltages are passed together, electric charge accumulates in the electric field between them; This effect is ingrained.

All practical circuit elements such as inductors , diodes , and transistors have internal capacitance, which can make their behavior different from that of ideal circuit elements. Additionally, there is always a non-zero capacitance between any two conductors; This can be important with closely spaced conductors, such as wires or printed circuit board traces. The parasitic capacitance between the windings of an inductor or other wound component is often described as self-capacitance . However, in electromagnetics, the term self-capacitance more correctly refers to a different phenomenon: the capacitance of a conductive object without reference to another object.

Parasitic capacitance is a significant problem in high-frequency circuits and is often the limiting factor in the operating frequency and bandwidth of electronic components and circuits.

## Description

When two conductors with different potentials are in close proximity to each other, they are affected by each other’s electric field and store opposite electric charges, like a capacitor. Changing potential V requires a current between the conductors I in or out of the conductors to charge or discharge them.

i=C{\frac {dv}{dt}}\,


where C is the capacitance between the conductors. For example, an inductor often acts as if it includes a parallel capacitor , because of its closely spaced winding . When a potential difference exists across the coil, the wires adjacent to each other have different potentials. They act like the plates of a capacitor, and store charge . Any change in voltage across the coil requires additional current to charge and discharge these tiny ‘capacitors’.is required. When the voltage changes only slowly, such as in a low-frequency circuit, the additional current is usually negligible, but when the voltage changes quickly the additional current is large and can affect the operation of the circuit.

The coils are often basket-wound for higher frequencies to reduce parasitic capacitance .

## Effect

At low frequencies parasitic capacitance can usually be ignored, but it can be a major problem in high frequency circuits. In amplifier circuits with extended frequency response, the parasitic capacitance between the output and the input can act as a feedback path, causing the circuit to vibrate at high frequencies. These unwanted oscillations are called parasitic oscillations .

In high frequency amplifiers, parasitic capacitance can combine with stray inductance such that the component forms a resonant circuit , which also causes parasitic oscillations. In all inductors, the parasitic capacitance will resonate with the inductance at some high frequency making 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 circuits connected to the outputs 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 of termination lines between inputs and outputs , and striplines of unwanted capacitance effects to reduce.

In closely spaced cables and computer buses , parasitic capacitive coupling can cause crosstalk , which means signals bleed from one circuit to 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 incorporate them into simulations of circuit operation. can. This is called parasite extraction .

### Miller capacitance

The parasitic capacitance between the input and output electrodes of inverting amplifying devices, such as between the base and collector of a transistor , is particularly troublesome because it is multiplied by the gain of the device. This Miller capacitance ( first noted in vacuum tubes by John Milton Miller , 1920) is the major factor limiting the high-frequency performance of active devices such as transistors and vacuum tubes . Screen grids were added to the triode control grid in the 1920s to reduce the parasitic capacitance between vacuum tubes and the plate, creating the tetrode, which resulted in a great increase in operating frequency.

The diagram, right, shows how the Miller capacitance is arrived at. Suppose the amplifier shown is an ideal inverting amplifier with a voltage gain of A , and Z = C a capacitance between its input and output. The output voltage of the amplifier is

v _ {{\text {o}}} = - Av _ {{\text {i}}}

Assuming that the amplifier itself has high input impedance so its input current is negligible, the current across the input terminal is

i_{{\text{i}}}=C{d \over dt}(v_{{\text{i}}}-v_{{\text{o}}})\,
i _ {{\text {i}}} = C {d \over dt} (v _ {{\text {i}}} + Av _ {{\text {i}}}) \,
i_{{\text{i}}}=C(1+A){dv_{{\text{i}}} \over dt}\,

So the capacitance at the input of the amplifier is

C_{{\text{M}}}=C(1+A)\,


The input capacitance is multiplied by the gain of the amplifier. This is Miller capacitance. If the input circuit has an impedance of R i to ground, then (assuming no other amplifier poles) the output of the amplifier is

V_{{\text{o}}}={\frac {A}{1+j\omega R_{{\text{i}}}C_{{\text{M}}}}}V_{{\text{i}}}\,

Amplifier’s bandwidth is limited by high frequency roll-off

f={1 \over 2\pi R_{{\text{i}}}C_{{\text{M}}}}={1 \over 2\pi R_{{\text{i}}}C(1+A)}\,


So the bandwidth factor is reduced by (1 + A ), approximately the voltage gain of the device. The voltage gain of modern transistors can be 10 – 100 or so, so this is a significant limitation.