FREQUENCY RESPONSEFREQUENCY RESPONSEELEC 202 Circuit Analysis II

IntroductionIntroductionThe frequency response of a circuit is the

variation in its behavior due to the change in signal frequency.

Measured in terms of the variation of the gain and phase as a function of frequency

Vary the frequency of the input signal source (i.e. sinusoid) while keeping its amplitude constant

Important in filter design

DefinitionDefinitionFor a circuit with a sinusoidal input

source, its frequency response is defined as the ratio of its phasor output to its phasor input, expressed as a function of frequency.

)()()()()(

jHjHjXjYjH

Types of Frequency ResponseTypes of Frequency ResponseGain Voltage )(

)()(

jVjVjH

i

o

Gain Current )()()(

jIjIjH

i

o

Impedance Transfer)()()(

jIjVjH

i

o

Admittance Transfer)()()(

jVjIjH

i

o

CharacteristicsCharacteristicsTypically expressed as an irreducible ratio

of two polynomials in frequency (i.e., the common numerator and denominator factors have canceled, reducing the ratio to the lowest terms)

When working with , temporarily replace with s to avoid complex algebra

jssDsNsH ,)(

)()(

j)( jH

Characteristics (Cont’d)Characteristics (Cont’d)Roots of the numerator polynomial are called the zeros of Roots of the denominator polynomial are called the poles of

)( jH)( jN

)( jD)( jH

Response Magnitude )()( jHjMResponse Phase )()( jHj

The Decibel ScaleThe Decibel ScaleThe use of a logarithmic scale to express

gain (either power, voltage or current)

The 10log is used for power, while 20log is used either for voltage or current.

The two quantities in the ratio must be of the same type.

1

210

1

210

1

210 log20log20log10

II

VV

PPGdB

ExampleFor the RC circuit shown, determine andsketch its frequency response.

Magnitude Response Phase response

ExampleFor the RL circuit shown, determine andsketch its frequency response.

Magnitude Response Phase response

ExampleFor the circuit shown, determine the gain and its poles and zeros.)(/)( jIjI io

ExampleFor the circuit shown, determine its transferimpedance and obtain its poles and zeros.