Help me to derive the OTA gm-C frequency

[Anachip]

Hi guys,

Please help me to configure how the equation of f=gm/2xpixC in derived from the basic 2 input OTA with Io output seeing a C load. If possible with the small signal analysis. I tried to derive it, but could so as there is no R load. Thanks.

 

[LvW]

Hi guys,

Please help me to configure how the equation of f=gm/2xpixC in derived from the basic 2 input OTA with Io output seeing a C load. If possible with the small signal analysis. I tried to derive it, but could so as there is no R load. Thanks.

Neglecting the real Rout of the OTA, the output voltage across C is Vout=Iout/jωC.
Wth Iout=Vin*gm you arrive at the integrator function
Vout/Vin=gm/jω*C.

At ω=gm/C the fuction has unity gain (cross over frequency).

Under real conditions with Rout finite the integrator approximates a low pass, but with only minor influence on the cross over frequency