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lhlbluesky_lhl

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Gm-c bandpass filter transient response
Oct 26^th, 2012, 6:14am

i have designed a Gm-C BPF, biquad type with two OTA and two Cap. i set gm1=gm2=gm=13uS (low power design), C2=100*C1=1nF, f0=gm/sqrt(C1*C2)=20kHz, Q=sqrt(C2/C1)=10, now, the ac response shows that, f0 and Q has some deviation (20.4KHz and 9.23), what is the possible reason here?

besides, for a Gm-C BPF, how is the transient response? does the OTA need slew rate and settling (the same as OPA)? if so, for a 1nF cap, it is very difficult for the OTA to settle well. am i right?

thanks all.

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buddypoor

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Re: Gm-c bandpass filter transient response
Reply #1 - Oct 26^th, 2012, 6:37am

lhlbluesky_lhl wrote on Oct 26^th, 2012, 6:14am:

i have designed a Gm-C BPF, biquad type with two OTA and two Cap. i set gm1=gm2=gm=13uS (low power design), C2=100*C1=1nF, f0=gm/sqrt(C1*C2)=20kHz, Q=sqrt(C2/C1)=10, now, the ac response shows that, f0 and Q has some deviation (20.4KHz and 9.23), what is the possible reason here?

besides, for a Gm-C BPF, how is the transient response? does the OTA need slew rate and settling (the same as OPA)? if so, for a 1nF cap, it is very difficult for the OTA to settle well. am i right?

thanks all.

Congratulation!
For my opinion, the mentioned deviation are rather small and it seems you have done a really good design.
The reason is obvious: I don`t know how exact the designed gm values are realized, but the main reason for the deviation surely is the finite output impedance of the OTA`s.

Regarding the transient response: This response does not depend on the selected technology (passiv, active, opamp or OTA).
The step response exhibits the classical damped sinusoidal wave, which is common for all high-Q systems.

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LvW (buddypoor: In memory of the great late Buddy Rich)

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lhlbluesky_lhl Senior Member Offline Posts: 115	Re: Gm-c bandpass filter transient response Reply #2 - Oct 26^th, 2012, 7:05am hi, buddypoor, thanks for your reply. i have another question, what is the relationship between the finite output impedance of the OTA and the real deviation? and why? besides, how to evaluate the step response of BPF? and is my design OK about the transient response aspect (small gm and large Cap)?
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buddypoor

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Re: Gm-c bandpass filter transient response
Reply #3 - Oct 26^th, 2012, 8:50am

lhlbluesky_lhl wrote on Oct 26^th, 2012, 7:05am:

hi, buddypoor, thanks for your reply.
i have another question, what is the relationship between the finite output impedance of the OTA and the real deviation? and why? besides, how to evaluate the step response of BPF? and is my design OK about the transient response aspect (small gm and large Cap)?

First question: There is no simple answer because each particular circuit topology reacts differently on finite output resistors. They act as damping resistors and, thus, explain why the Q is lower than desired. There is no other way than to find the transfer function without neglecting the finite Rout.
This can be accomplished also by a symbolic simulation program.
But don`t forget: You also have neglected the frequency-dependence of the transconductance. This may have caused also some deviations.

Second question: The bandpass step response for several Q values can be found in each relevant textbook on filter design. It is a damped sinusoidal function (damping invers proportional to Q).

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LvW (buddypoor: In memory of the great late Buddy Rich)

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lhlbluesky_lhl

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Re: Gm-c bandpass filter transient response
Reply #4 - Oct 27^th, 2012, 6:58am

i have uploaded the BPF fig, TFS and GFS. but i have some questions in transient simulation.
1, for TFS, the AC response shows that, f0=20.4KHz(ideal 20KHz), Q=9.23(ideal 10), H0=0.5(ideal 1). when transient simulation(an AC coupling cap added before VIN), the virtual ground is 0.8V(positive input of g1 and negative input of g2), and i add a 20KHz sine wave(0 to 0.2V pk-pk), but vout is only 0.5V or so (and very slowly increasing). why? any mistakes here? C1=10pF, C2=1nF, gm1=gm2=gm3=13uS.
2, for GFS, the AC response shows that, f0=20.5KHz(ideal 20KHz), Q=9.28(ideal 10), H0=0.4(ideal 1). when transient simulation(an AC coupling cap added before VIN), the virtual ground is 0.8V also, and i add a 20KHz sine wave(0 to 0.2V pk-pk), but vout is only 0.2mV pk-pk sine wave(dc offset=0.78V, not 0.8V). and why H0 becomes so small (1/1000)? any mistakes here? C1=10pF, C2=1nF, gm1=gm2=gm3=13uS.
thanks.

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lhlbluesky_lhl

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Re: Gm-c bandpass filter transient response
Reply #5 - Oct 29^th, 2012, 5:52am

in my ac simulation, H0=0.95(ideal = 1), but in transient simulation, it is only 0.1 (a little increase with decreasing of input pk-pk), what is the non-ideal factor of influencing H0 in transient simulation? slew rate and bandwidth? in my view, f0=gm/C, and gm and C are proportional, if i increase gm, C will increase the same amount, to make constant f0. so, how to consider settling of OTA (and the whole BPF)?
besides, if i use switched-cap structure for BPF design, what is the proper choice, MFB, sallen-key, or others? and how to simulate the ac characteristic of switched-cap BPF (with two clock phase at least)? such as AC response, noise, thd, etc.
for the f0 control, we can change the clock frequency of swithes, the clock can be generated by an frequency-tuning oscillator, and any other methods to generate switched clock?
thanks.

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buddypoor

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Re: Gm-c bandpass filter transient response
Reply #6 - Oct 29^th, 2012, 8:47am

Ihlbluesky, did you check the basic properties of the used OTA`s ?
-Input/output impedances,
-frequency dependence of the transconductance gm
- slewing behaviour.

Without knowing these data an answer is impossible.
What is the source of the used filter topologies?
BTW: Please explain the used abbreviations Ho, TFS, GFS

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LvW (buddypoor: In memory of the great late Buddy Rich)

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lhlbluesky_lhl

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Re: Gm-c bandpass filter transient response
Reply #7 - Oct 30^th, 2012, 6:11am

gm is almost constant with frequency.
H0 is the pass-band max gain when f=f0, TFS and GFS are just as the fig shows, three-OTA BPF and four-OTA BPF.
besides, i now found that, in ac simulation, there is a LHP zero at low frequency, i think it is generated by the finite output resistance of OTA, right? and can this zero have an influence on the transient response of the BPF above mentioned?

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