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Switched Capacitor Integrator Question

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mrcupido

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Shown is the test circuit for a switched capacitor circuit. From the plot waveform, the output for a square wave input is a triangle waveform.
However, the closed loop gain is supposed to be 0.5 because of the ratio Cs/Cf, but my output results to have a gain of 250. Could anyone help me fix the closed loop gain?

Op-Amp Specfication:

Folded Cascode w/ Class AB Output Stage and Gain Boosting
DC Gain: 25,000
GBW: 150 MHZ
SR: ~ 40 V/us

I also tried it with a simpler amplifier (Folded Cascode with Gain Boosting w/o Output Stage), DC Gain = 1,300
but it still has a gain instead of attenuation.

The non overlapping clock has a frequency of 20.48 MHZ, and the input signal is 10 KHZ.

P.S. : Vbias4 of the amplifier is for the SC-CMFB.

Thanks for the help.

integratorschematic.png
integratorplot.png
 

Please, verify the expected gain of 0.5; what are the capacitor values (cannot be identified in the drawing) ?
Recommendation: Check the integrator function with a sinusoidal signal (frequency identical to 1/T with T=integrator time constant)
 

Capacitor Values are Cs = 2 pF and Cf = 4 pF.

When using a sinusoid, the output is a cosine with amplified gain. My only problem is the gain. The signal is being amplified instead of being attenuated to 0.5 of the Input.

Also, both amplifiers used are stable. (Phase Margins are 75 and 40 degrees)
 
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Capacitor Values are Cs = 2 pF and Cf = 4 pF.

When using a sinusoid, the output is a cosine with amplified gain. My only problem is the gain. The signal is being amplified instead of being attenuated to 0.5 of the Input.

For an S/C integrator the capacitor ratio Cs/Cf is equal to Tcl/Ti with Tcl=1/Fclock and Ti=Integrator time constant=1/w,co (w,co=cross-over frequency with unity gain).

In your case: Ti=Tcl*4/2=2*Tcl=1E-7 sec.
Thus w,co=1E7 rad7sec >>> F,co=1.6 MHz.

In words: The transfer function crosses the 0dB-line at F,co=1.6 MHz.
Because your signal frequency is much smaller (10 kHz) the circuit has, of course, gain.
According to my calculations, you should measure a unity gain for a signal frequency of app. 1.6 MHz.
If you like to have unity gain at 10 kHz the integrator time constant must be reduced correspondingly.
 

For an S/C integrator the capacitor ratio Cs/Cf is equal to Tcl/Ti with Tcl=1/Fclock and Ti=Integrator time constant=1/w,co (w,co=cross-over frequency with unity gain).

In your case: Ti=Tcl*4/2=2*Tcl=1E-7 sec.
Thus w,co=1E7 rad7sec >>> F,co=1.6 MHz.

In words: The transfer function crosses the 0dB-line at F,co=1.6 MHz.
Because your signal frequency is much smaller (10 kHz) the circuit has, of course, gain.
According to my calculations, you should measure a unity gain for a signal frequency of app. 1.6 MHz.
If you like to have unity gain at 10 kHz the integrator time constant must be reduced correspondingly.

Thank you for your response. However, I'm not aware of the equality of Cs/Cf with Tcl/Ti. Could you suggest any book/reference for that?

Also, how can I make my the integrator time constant smaller without varying the sampling frequency? I was basing my assumptions on the paper by Boser and Wooley regarding Sigma Delta Modulator in which they used Cs/Cf equal to 0.5. This was the case because I needed to implement an oversampling ratio of 512.

Thanks for your time.
 

The time constant of the corresponding analog integrator is
Ti=Rs*Cf

Replacing Rs by a switched cap gives Rs=1/(Fcl*Cs)

Thus, you easily arrive at Ti=Tcl*Cf/Cs.

I think, for changing Ti it shouldn't be a problem for you to select other values for Cf or Cs.
 
Thank you! Though I'm not sure if it will work properly if the integrator is using the same Sampling frequency and input frequency since the integrator should operate in the sigma delta modulator with Oversampling ratio of 512. Different papers always suggest that the closed loop gain is Cs/Cf in a sigma delta modulator and i couldnt show the 0.5 gain.
 

Thank you! Though I'm not sure if it will work properly if the integrator is using the same Sampling frequency and input frequency....

???
I never told you something like this. The given formulas don't show any signal frequency.
If you like to operate in the vicinity of the cross-over frequency (Tsignal approx. equal to Ti) with a gain around unity the ratio Ti/Tcl=Cf/Cs must be chosen sufficient small - that's all.

---------- Post added at 15:24 ---------- Previous post was at 15:19 ----------

Quote: Different papers always suggest that the closed loop gain is Cs/Cf

Don`t mix the gain of a S/C amplifier (which, indeed, is Cs/Cf) with gain of an integrating stage.
 
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