Case: internally compensated opamp with a pole-splitting capacitor

 

Small input signals:       -    transistors operate in their saturation regions

-         small-signal models can be used

-         for moderate frequencies (­­|s_p1| << w << ­­|s_p2|)

o       input stage Q₁ - Q₅ can be replaced by a frequency-independent voltage controlled  current source

o       stages Q₆ - Q₁₁ can be replaced by a frequency-independent amplifier with the feedback capacitor C_c connected between its input and output terminals

o       corresponding model:

 

 

 

 

High-frequency gain:

                      

 

Unity-gain frequency:

                      

 

 

Case: voltage inverter

 

 

Supposing a step voltage on the input:

Output voltage

            For small input amplitude (much less than 1 V):

            Exponentially varying waveform

 

 

            For large input amplitude ( ~ 5 V):

            Nearly linear rise and fall slewing

 

 

 

Slew rate ... slope                                               

 

w₀  ...   Unity gain frequency

I₀   ...   Bias current of the input stage

L   ...    Length of the channel

W  ...   Width of the channel

 

Related Reading

Gregorian, R., Temes G. C., Analog MOS integrated circuits for signal processing, Wiley, 1986.

Johns, D. A., Martin, K., Analog integrated circuit design, Wiley, 1997.

Razavi, B., RF Microelectronics, Prentice Hall, 1998.

Carter, B., Brown, T.R., Handbook of operational amplifier applications, Application Report, Texas Instreuments, 2001.