cl254
Junior Member level 2
Hi All,
In a two-stage amp with capacitive feedback, the closed loop circuit 3dB frequency (closed loop bandwidth) is equal to cut-off (crossover) frequency of the loop gain (T(s)) --> w(-3dB)_CL = wc_T
What is the cut-off frequency of the closed loop circuit (wc_CL)? Somehow the wc_CL equals (return factor)*wc_T, let me try to explain it below and please let me know whether it makes sense, if not please let me know what you think.
In the open loop circuit, say the open loop gain is ao, and the dominant pole (single pole approximation is valid) is wp1.
Say the return factor = beta.
In the closed loop circuit, the closed loop gain is ao/(1+ao*beta), and the closed loop circuit bandwidth, w(-3dB)_CL, now becomes wp1*(1+ao*beta) ~= wp1*ao*beta = beta*GBW_openloop = wc_T (this corresponds to the first line of this message)
And since the closed loop gain, ao/(1+ao*beta) ~=ao/(ao*beta) = 1/beta and is very small compared to ao, the the closed loop circuit 3dB frequency (w(-3dB)_CL) is approximately the same as the closed loop circuit cut-off (crossover) frequency (wc_CL), so w(-3dB)_CL ~= wc_CL, is this correct???
Thank you very much.
In a two-stage amp with capacitive feedback, the closed loop circuit 3dB frequency (closed loop bandwidth) is equal to cut-off (crossover) frequency of the loop gain (T(s)) --> w(-3dB)_CL = wc_T
What is the cut-off frequency of the closed loop circuit (wc_CL)? Somehow the wc_CL equals (return factor)*wc_T, let me try to explain it below and please let me know whether it makes sense, if not please let me know what you think.
In the open loop circuit, say the open loop gain is ao, and the dominant pole (single pole approximation is valid) is wp1.
Say the return factor = beta.
In the closed loop circuit, the closed loop gain is ao/(1+ao*beta), and the closed loop circuit bandwidth, w(-3dB)_CL, now becomes wp1*(1+ao*beta) ~= wp1*ao*beta = beta*GBW_openloop = wc_T (this corresponds to the first line of this message)
And since the closed loop gain, ao/(1+ao*beta) ~=ao/(ao*beta) = 1/beta and is very small compared to ao, the the closed loop circuit 3dB frequency (w(-3dB)_CL) is approximately the same as the closed loop circuit cut-off (crossover) frequency (wc_CL), so w(-3dB)_CL ~= wc_CL, is this correct???
Thank you very much.
