Parasitic capacitance

Parasiticcapacitanceorstray capacitanceis the unavoidable and usually unwantedcapacitancethat exists between the parts of anelectronic componentorcircuitsimply because of their proximity to each other. When twoelectrical conductorsat different voltages are close together, the electric field between them causeselectric chargeto be stored on them; this effect is capacitance.

All practicalcircuit elementssuch asinductors,diodes,andtransistorshave internal capacitance, which can cause their behavior to depart from that of ideal circuit elements. Additionally, there is always some capacitance between any two conductors; this can be significant with closely spaced conductors, such as adjacent wires orprinted circuit boardtraces. The parasitic capacitance between the turns of an inductor (e.g. Figure 1) or other wound component is often described asself-capacitance.However, in electromagnetics, the termself-capacitancemore 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 factor limiting the operatingfrequencyandbandwidthof electronic components and circuits.

Description

When two conductors at differentpotentialsare close to one another, they are affected by each other'selectric fieldand store oppositeelectric charges,forming a capacitor.^[1]Changing the potential $V$ between the conductors requires a current $i$ into or out of the conductors to charge or discharge them:^[2]

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

where $C$ is the capacitance between the conductors. For example, aninductoroften acts as though it includes a parallelcapacitor,because of its closely spacedwindings.When apotentialdifference exists across the coil, wires lying adjacent to each other are at different potentials. They act like the plates of a capacitor, and storecharge.Any change in the voltage across the coil requires extracurrentto charge and discharge their small capacitances. When the voltage changes only slowly, as in low-frequency circuits, the extra current is usually negligible, but when the voltage changes quickly the extra current is larger and can affect the operation of the circuit.

Coils for high frequencies are oftenbasket-woundto minimize parasitic capacitance.

Effects

At lowfrequenciesparasitic capacitance can usually be ignored, but in high frequency circuits it can be a major problem. Inamplifiercircuits with extended frequency response, parasitic capacitance between the output and the input can act as afeedbackpath, causing the circuit tooscillateat high frequency. These unwanted oscillations are calledparasitic oscillations.

In high frequency amplifiers, parasitic capacitance can combine with stray inductance such as component leads to formresonant circuits,also leading to parasitic oscillations. In all inductors, the parasitic capacitance will resonate with the inductance at some high frequency to make the inductorself-resonant;this is called theself-resonant frequency.Above this frequency, the inductor actually hascapacitive reactance.

The capacitance of the load circuit attached to the output ofop ampscan reduce theirbandwidth.High-frequency circuits require special design techniques such as careful separation of wires and components, guard rings,ground planes,power planes,shieldingbetween input and output,terminationof lines, andstriplinesto minimize the effects of unwanted capacitance.

In closely spaced cables andcomputer busses,parasitic capacitive coupling can causecrosstalk,which means the signal from one circuit bleeds into another, causing interference and unreliable operation.

Electronic design automationcomputer programs, which are used to design commercialprinted 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 calledparasitic extraction.

Miller capacitance

Figure 1: TheMiller effectcauses 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}

.

Assume the ideal inverting amplifier withgainof $A_{\nu }$ 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 infiniteinput 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 theMiller effectmultiplies 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 theangular frequency $\ Omega =2\pi f$ .This acts as alow-pass filterwith acutoff frequencythat limits the amplifier'sbandwidthto:

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 forop ampsare orders of magnitudes higher, soMiller capacitance(first noted invacuum tubesbyJohn Milton Millerin 1920) is a significant limitation on the high frequency performance of amplifying devices. Thescreen gridwas added totriodevacuum tubes in the 1920s to reduce parasitic capacitance between thecontrol gridand theplate,creating thetetrode,which resulted in a great increase in operating frequency.^[3]Inbipolar junction transistors,the parasitic capacitances between the base and collector or emitter have voltage dependence too.^[4]

References

^Glisson, Tildon H. (2011).Introduction to Circuit Analysis and Design.Springer Science and Business Media. p. 255.ISBN 9789048194438.
^Sangwine, S. J. (1994).Electronic Components & Technology, 2nd Edition.CRC Press. pp.115–118.ISBN 9780748740765.
^Alley, Charles L.; Atwood, Kenneth W. (1973).Electronic Engineering, 3rd Ed.New York: John Wiley & Sons. p. 199.ISBN 0-471-02450-3.
^https://my.ece.msstate.edu/faculty/winton/CDNuE/SoftCopy/ch12.pdf^{[bare URL PDF]}

[Glisson-1] Glisson, Tildon H. (2011).Introduction to Circuit Analysis and Design.Springer Science and Business Media. p. 255.ISBN 9789048194438.

[Sangwine-2] Sangwine, S. J. (1994).Electronic Components & Technology, 2nd Edition.CRC Press. pp.115–118.ISBN 9780748740765.

[3] Alley, Charles L.; Atwood, Kenneth W. (1973).Electronic Engineering, 3rd Ed.New York: John Wiley & Sons. p. 199.ISBN 0-471-02450-3.

[4] ttps://my.ece.msstate.edu/faculty/winton/CDNuE/SoftCopy/ch12.pdf^{[bare URL PDF]}

[1]

[2]

[3]

[4]