On the Operation of CMOS Active- Cascode Gain Stage Victor Lu, William Eisenhower, Yun Chiu Illinois Center fo Wireless Systems Active Cascode Benefits: • High DC gain • High bandwidth • Low power implementation Issues: • Pole-Zero Doublet • Settling Issues Pole-Zero Doublet • Closely spaced pole and zero near unity gain bandwidth of auxiliary amplifier • Zero is from auxiliary amplifier shorting out reducing output resistance • Pole is from cascode output Settling Concerns • Pole-Zero doublet can cause slow settling • Rapid settling until regular cascode gain • Slow from there until final value •Rate Depends on relative spacing of doublet •Wider the spread slower the settling •If no doublet, amplifier settles rapidly to final value Modeling Doublet ωo= AA dominate pole ωa= AA unity gain bandwidth ωu= cascode unity gain bandwidth x= ω3/ ωo Canceling Doublet • It is possible to cancel doublet exactly • Requires ration of unity gain bandwidths so that the cancel out the slow settling component Simulation Model Small-signal linear model including some second- order effects Simulation Results Simulation Results Closed loop settling behavior for auxiliary amplifier bandwidth of 10 kHz, 100 kHz, 1 MHz, 5 MHz, 9 MHz, 10.95 MHz, 20 MHz, 30 MHz Dashed curves are for first-order model V o V 2 V 1 X Y r o2 C gs2 r o1 g m2 V 2 g m1 V 1 C o C gd2 C gd1 C m -A a (s) C gs1 |A a (jω )| ω (log) |A tot | (log) ~A a A o A t ω o ω a ω 3 ω 1 ω 2 ω u ~A 1 ~A 2 Doublet A tot (jω )= G m ,eff (jω )·Z tot (jω) O ut V B In M 2 M 1 A a (s) X I B C o Y Auxiliary Amp (AA) ω (log) |Z tot | (log) ~A a r o1 r o R o ω o ω a ω 3 ω 1 ω 2 ω u Z tot (jω )= Z o (jω )//(jω C o ) -1 |Z o (jω )| (ωC o ) -1 A B r o C o /x C o C o /x C o A a r o A B 2 2 2 1 2 2 2 2 2 11 11 2 2 1 1 2 12 1 1 1 1 1 0 o m o o a a u o o a m o mo mo m o o o u mo a r g r r A k r r g r g r Ag r g r r r k g r