ECE 342 Electronic Circuits Lecture 26 Frequency Response of Cascaded Amplifiers Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois [email protected] ECE 342 –Jose Schutt‐Aine 1 CE Cascade Amplifier Exact analysis too tedious use computer CE cascade has low upper‐cutoff frequency ECE 342 –Jose Schutt‐Aine 2 MOS Cascode Amplifier Common source amplifier, followed by common gate stage – G2 is an incremental ground 1 Define go1 ro1 1 go2 ro2 1 GL RL RL current source impedance ECE 342 –Jose Schutt‐Aine 3 MOS Cascode Amplifier • CS cacaded with CG Cascode Very popular configuration Often considered as a single stage amplifier • Combine high input impedance and large transconductance in CS with current buffering and superior high frequency response of CG • Can be used to achieve equal gain but wider bandwidth than CS • Can be used to achieve higher gain with same GBW as CS ECE 342 –Jose Schutt‐Aine 4 MOS Cascode Incremental Model iL vo GL igvgvvvgL mb22 s m 22 s s 2 o o 2 iL ivgLsmbm22 g 2 vg so 22 g o 2 GL ECE 342 –Jose Schutt‐Aine 5 MOS Cascode Analysis go2 ivgggLsmbmo122 22 GL igGLoL1/ 2 vs2 gggmb222 m o KCL at vs2 gvmgs121222222 v s g o g m v s g mbs v g o()0 v s v o ECE 342 –Jose Schutt‐Aine 6 MOS Cascode Analysis ggGooL121/ gvmgs1110 i L ggommb22 g 2 gvmgs11 iL ggGooL121/ 1 ggommb22 g 2 vg om 1 vin gGoL12 g o GL ggommb22 g 2 Two cases ECE 342 –Jose Schutt‐Aine 7 MOS Cascode Analysis CASE 1 Case1: If GL 0 The voltage gain becomes vo ggmo12 g m 2 g mboo 212 rr vin AggggggrrMBmommmmboo12 1 2 1 2 12 AgrgrMBmomo 11 2 2 ECE 342 –Jose Schutt‐Aine 8 MOS Cascode Analysis CASE 2 gGoL12 g o Case2: If GL ggommb22 g 2 The voltage gain becomes vgom 1 AMB vGin L ECE 342 –Jose Schutt‐Aine 9 MOS Cascode at High Frequency The upper corner frequency of the cascode can be approximated as: 1 f2o where CC22233 db Cgddb C Cgd 2 rCds32 ECE 342 –Jose Schutt‐Aine 10 MOS Cascode at High Frequency • Capacitance Cgs1 sees a resistance Rsig • Capacitance Cgd1 sees a resistance Rgd1 • Capacitance (Cdb1+Cgs2) sees resistance Rd1 • Capacitance (CL+Cgd2) sees resistance (RL||Rout) 1 RL R1gRRRgd1 m1 d1 sig d1 Rrd1 o1 ggm2 mb2 A vo2 HCR gs1 sig C gd1 1gR m1 d1 R sig R d1 CCRCCRRdb1 gs2 d 1 L gds2 L out 1 fH 2 H ECE 342 –Jose Schutt‐Aine 11 MOS Cascode at High Frequency If Rsig is large, to extend the bandwidth we must lower RL. This lowers Rd1 and makes the Miller effect insignificant If Rsig is small, there is no Miller effect. A large value of RL will give high gain ECE 342 –Jose Schutt‐Aine 12 Effect of Cascoding (when Rsig=0) ECE 342 –Jose Schutt‐Aine 13 BJT Cascode Amplifier Common emitter amplifier, followed by common base stage – Base of Q2 is an incremental ground ECE 342 –Jose Schutt‐Aine 14 Cascode Amplifier First stage is CE and second stage is CB If Rs << r1, the voltage gain can be approximated by AvmL gR12 ECE 342 –Jose Schutt‐Aine 15 BJT Cascode Incremental Model vomLg 22Rv vrxx 22 r vvv 22 x 1 rrx22 r 2 ECE 342 –Jose Schutt‐Aine 16 BJT Cascode Analysis vx gvmm11 gv 2 2 rr 22 x Ignoring rx2 v 2 gvmm11 gv 2 2 r 2 1 gvmm11 v 2 g 2 r 2 ECE 342 –Jose Schutt‐Aine 17 BJT Cascode Analysis r1 vv1 in Rsxrr11 grvmin11 1 v 2 Rrsx11 r 1 gm2 r 2 gRgrvmLm211 in 1 vo Rrsx11 r 1 gm2 r 2 ECE 342 –Jose Schutt‐Aine 18 BJT Cascode Analysis vgrgrR ommL 22 11 vRrrgrin s x111 m 22 v R o 12L vRrrin s x112 1 If Rs << rx1+r1, the voltage gain can be approximated by AvmL gR12 ECE 342 –Jose Schutt‐Aine 19 BJT Cascode at High Frequency Define rcs as the internal impedance of the current source. R includes generator resistance and base resistance rx1 base of Q1 ECE 342 –Jose Schutt‐Aine 20 BJT Cascode at High Frequency There is no Miller multiplication from the input of Q2 (emitter) to the output (collector). ECE 342 –Jose Schutt‐Aine 21 BJT Cascode at High Frequency Define R32 rout r cs 111 AA MB 111jC11 r R jrCeout 22 jRC 3 1 1 fin high f2 2 rRC11 2 rCe22 11 AA MB f f 11jj ffin high out high ECE 342 –Jose Schutt‐Aine 22 BJT Cascode at High Frequency 1 fout high 2CRout 3 CCout out2 C outcs Coutcs current source output capacitance ECE 342 –Jose Schutt‐Aine 23 Cascode Amplifier – High Frequency High‐frequency incremental model ECE 342 –Jose Schutt‐Aine 24 Cascode Amplifier – High Frequency Applying Kirchoff’s current law to each node: GV'' G g s C C V sC V s is1 11a1b 0g sCVg g sCC V g g sCV m11a 2m22 1b 2m22d 0gsCVggsCCVsCV 22bx22 22d2o 0 gm2 V b g m2 sC 2 V d G L sC 2 V o Find solution using a computer ECE 342 –Jose Schutt‐Aine 25 Cascode Amplifier – High Frequency As an example use: gm=0.4 mhos =100 r=250 ohms rx=20 ohms C=100 pF C=5 pf GL=5 mmhos GS’=4.5 mmhos ZEROS (nsec‐1) POLES (nsec‐1) sa=8.0 sd=‐0.0806 sb=‐2.02 + j5.99 se=‐0.644 sc=‐2.02 – j5.99 sf=‐4.05 sg=‐16.45 ECE 342 –Jose Schutt‐Aine 26 Cascode Amplifier – High Frequency If one pole is at a much lower frequency than the zeros and the other poles, (dominant pole) we can approximate 3dB 9 3dB 0.0806 10 rad / sec f3dB 12.9 MHz For the same gain, a single stage amplifier would yield: 9 3dB 0.0169 10 rad / sec f3dB 2.7 MHz Second stage in cascode increases bandwidth ECE 342 –Jose Schutt‐Aine 27.