Transferfunction:poles,zerosMost of our work in this chapter will be concerned withfinding amplifier voltage gain as a transfer function ofthe complex frequency s.> A capacitance C: is equivalent an impedance 1/sC An inductance L: is equivalent an impedance SL> Voltage transfer function: by replacing S by jw, wecan obtain its magnitude response and phaseresponsem-1+...+aoT(s) = V.(s)/ V(s) =+br-isn-l +...+boYMicroelectronicCircuits
Microelectronic Circuits Transfer function: poles, zeros ➢ Most of our work in this chapter will be concerned with finding amplifier voltage gain as a transfer function of the complex frequency s. ➢ A capacitance C: is equivalent an impedance 1/SC ➢ An inductance L: is equivalent an impedance SL ➢ Voltage transfer function: by replacing S by jw, we can obtain its magnitude response and phase response 0 1 1 0 1 1 . . ( ) ( )/ ( ) s b s b a s a s a T s V s V s n n n m m m m o i + + + + + + = = − − − −
Transferfunction:poles,zeros(s - Z,)(s- Z,)......(s -ZmT(s) = V.(s)/V(s) = an(s - P)(s - P)......(s - P)Z1, Z2, ... Zm are called the transfer-function zeros ortransmission zeros.> P1, P2, ... Pm are called the transfer-function poles ornatural modes.The poles and zeros can be either real or complexnumbers, the complex poles(zeros) must occur inconjugate pairs.Microelectronic Circuits
Microelectronic Circuits Transfer function: poles, zeros ➢ Z1, Z2, . Zm are called the transfer-function zeros or transmission zeros. ➢ P1, P2, . Pm are called the transfer-function poles or natural modes. ➢ The poles and zeros can be either real or complex numbers, the complex poles(zeros) must occur in conjugate pairs. ( )( ).( ) ( )( ).( ) ( ) ( )/ ( ) 1 2 1 2 n m o i m s P s P s P s Z s Z s Z T s V s V s a − − − − − − = =
First-order Functions All the transfer functionsa,s+aoencountered in this chapterT(s)= have real poles and zeros ands+のocan be written as the product offirst-order transfer functionsao> Wo, called the pole frequency, isLow pass :T(s) =-s+0equal to the inverse of the timeconstant of circuita,sHigh pass : T(s) =network(STC).s+0oMicroelectronic Circuits
Microelectronic Circuits First-order Functions ➢ All the transfer functions encountered in this chapter have real poles and zeros and can be written as the product of first-order transfer functions. ➢ ω0, called the pole frequency, is equal to the inverse of the time constant of circuit network(STC). 0 1 0 ( ) + + = s a s a T s 0 1 0 0 High pass: ( ) Low pass: ( ) + = + = s a s T s s a T s
Example1:High pass circuit1A,Af0.707fiO+Q+(F)0f0.2p90°f00@ = 90°-arctan45°fi0°f(b)(a)R1joRCRCs7sT(s)11URCs +1S+1/ RCjoRC +1+RjoRCjwc11OLfrRC is the time constant; wL=1/RC2元2元T2元RCMicroelectronic Circuits
Microelectronic Circuits Example1: High pass circuit 2 1 + = • L L u f f f f A s RC s RCs RCs j RC j RC T s 1 1 1/ ( ) + = + = + = L f f = 90 − arctan RC is the time constant; ωL=1/RC
Example2: Low pass circuit1RO+ajac1IT十11+jaRCU;+ R0Ujac0O1/ RC[Aul S +1/ RC1RCisthetimeconstant;WH=1/RC0.70701LfH00°-45°f@=-arctan-90°fHMicroelectronic Circuits
Microelectronic Circuits Example2: Low pass circuit s RC RC T s 1/ 1/ ( ) + = H f f = −arctan RC is the time constant; ωH=1/RC 2 1 1 + = • H u f f A