TheGainFunctionA(s)= AμF(s)Fh(s)Gain functionMidband: No capacitors in effectA(s) ~ AMLow-frequencyband:couplingandbypasscapacitors in effectA(s) ~ AmF(s)High-frequency band: transistor internal capacitorsin effectA(s) ~ AMFμ(s)MicroelectronicCircuits
Microelectronic Circuits The Gain Function ⚫ Gain function ⚫ Midband: No capacitors in effect ⚫ Low-frequency band: coupling and bypass capacitors in effect ⚫ High-frequency band: transistor internal capacitors in effect A(s) A F (s) M H A(s) A F (s)F (s) = M L H A(s) A F (s) M L AM A(s)
The low-Frequency Gain FunctionGainfunctionA(s)= AmF(s)(s +0z1)(s +0z2)..(s + 0)-F(s)=S +0pls + 0p2).s+0.pnl...wpn are positive numbersWp1,Wp2,representing the frequencies of the n real polesWz1, Wz2, ....Wzn are positive, negative, or zeronumbers representing the freguencies of the nrealtransmissionzeros.Microelectronic Circuits
Microelectronic Circuits The low-Frequency Gain Function ⚫ Gain function ⚫ ωP1 , ωP2 , .ωPn are positive numbers representing the frequencies of the n real poles. ⚫ ωZ1 , ωZ2 , .ωZn are positive, negative, or zero numbers representing the frequencies of the n real transmission zeros. ( )( ) ( ) ( )( ) ( ) p p pnL Z Z ZnL L M L s s s s s s F s A s A F s + + + + + + = = . . ( ) ( ) ( ) 1 2 1 2
Determining the 3-dB FrequencyDefinitionorA(o,)= Aμ -3dBA(@ Assume Wp1< Wp2 < ... .<Wpn and Wz1 < Wz2<....<wzn+...-2(@zl+0z2-OL=Vのp1+のp2Microelectronic Circuits
Microelectronic Circuits Determining the 3-dB Frequency ⚫ Definition or ⚫ Assume ωP1< ωP2 < .<ωPn and ωZ1 < ωZ2 < .<ωZn 2 ( ) M L A A(L ) = AM −3dB A = . 2( .) 2 2 2 1 2 2 2 L P1 +P + − Z +Z +
Determining the 3-dB FrequencyDominant poleIf the lowest-frequency pole is at least two octaves(a factor of 4) away from the nearest pole or zero, itis called dominant pole. Thus the 3-dB frequency isdetermined by the dominant pole.Singlepolesystem,ACSs +plOL = plMicroelectronic Circuits
Microelectronic Circuits Determining the 3-dB Frequency ⚫ Dominant pole If the lowest-frequency pole is at least two octaves (a factor of 4) away from the nearest pole or zero, it is called dominant pole. Thus the 3-dB frequency is determined by the dominant pole. ⚫ Single pole system, 1 1 ( ) L P P M s A s A s + =
The High-Frequency Gain FunctionGain functionA(s) = AmFμ(s)(1+ s/0z1)(1+ s/@z2)..+F.(s)(1 + s/0p1)(1 + s/0p2)...(1 + s/0pn)Wp1, Wp2, ... .Wpn are positive numbersrepresenting the frequencies of the n real polesWz1 , Wz2 , ... .Wzn are positive, negative, or infinitenumbers representing the frequencies of the nrealtransmissionzeros.MicroelectronicCircuits
Microelectronic Circuits The High-Frequency Gain Function ⚫ Gain function ⚫ ωP1 , ωP2 , .ωPn are positive numbers representing the frequencies of the n real poles. ⚫ ωZ1 , ωZ2 , .ωZn are positive, negative, or infinite numbers representing the frequencies of the n real transmission zeros. (1 )(1 ).(1 ) (1 )(1 ).(1 ) ( ) ( ) ( ) 1 2 1 2 P P P n Z Z Zn H M H s s s s s s F s A s A F s + + + + + + = =