# Gain bandwidth issue of fully differential amplifier

1. ## Gain bandwidth issue of fully differential amplifier

Dear Friends,

I finished with the design of single ended OTA. the GBW was achieved is 20 MHz by driving capacitive load of 10 PF. Now I chnaged the design to fully differential OTA and I kept exactly the same biasing current or circuit transistor ratios, then I connected the smae load of 10 PF differentially between the two outputs to make a comparesion between the single and fully differential amplifier performance, I have found that differential amplifier is loosing half of the GBW ( =10MHz).

This leads me to reinvistigate the formula of GBW = gm1/2 pi CL for single ended,,, does it mean that GBW = 2gm1/2 pi CL for fully differential ampliifier ?

Or you have different explanation for this case

Thank you

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2. ## Re: Gain bandwidth issue of fully differential amplifier

This is hardly a mystery. Since you say you've kept everything the same as in the single-ended case, that means you have the same single ended voltages with respect to ground at the outputs but with opposite polarity to each other. You have connected the cap deferentially. It has the same ac current as in the single ended case defined by gm but it sees now double the voltage across it - since it is differential. That is, the same current has to charge the same cap to 2x bigger voltage and of course the GBW drops by 2x.
From another point of view - think about the Miller effect. Voltage on one side of the cap goes up, on the other side same amount goes down and hence the differential output sees 2x bigger cap.
Think from a third point of view. Differential cap C is equivalent to two series connected caps of 2C. Now, connect the middle point of the series connected caps to ground and you get the equivalent situation of yours but with 2 single ended caps from each output to ground. This is like running your single-ended OTA with a load cap of 2C, and hence again the GBW is 2x lower.

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3. ## Re: Gain bandwidth issue of fully differential amplifier

Originally Posted by sutapanaki
This is hardly a mystery. Since you say you've kept everything the same as in the single-ended case, that means you have the same single ended voltages with respect to ground at the outputs but with opposite polarity to each other. You have connected the cap deferentially. It has the same ac current as in the single ended case defined by gm but it sees now double the voltage across it - since it is differential. That is, the same current has to charge the same cap to 2x bigger voltage and of course the GBW drops by 2x.
From another point of view - think about the Miller effect. Voltage on one side of the cap goes up, on the other side same amount goes down and hence the differential output sees 2x bigger cap.
Think from a third point of view. Differential cap C is equivalent to two series connected caps of 2C. Now, connect the middle point of the series connected caps to ground and you get the equivalent situation of yours but with 2 single ended caps from each output to ground. This is like running your single-ended OTA with a load cap of 2C, and hence again the GBW is 2x lower.
Dear Suta,

So according to your answer that what I am getting is correct, that is the GBW of the fully differential amplifier is half of the identical single-ended counterpart with the same load condition,

Then why Allen Holberg is still using the formula of GBW = gm / 2 pi CL, where CL is the differential one, it should be 0.5 gm/ 2 pi CL ?

to make it more clear down is what I have simulated,

by the way, you see I am using high current of 120 uA to bias the OTA and still my GBW is very normal, I see a lot of people having several hundred MHz, if I kill myself I will not get such value, I am using 0.35 um technology and in my design i use channel length of 1 um

Thanks

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4. ## Re: Gain bandwidth issue of fully differential amplifier

OK, let's get into some details, then. Is your OTA 1 stage or two stage? If it is 2 stages, then your BW is really determined by the miller cap, not the load cap. Load cap only affects the 2nd pole. How about the CMFB? Is it working properly and does it maintain the wanted CM voltage? Maybe it is good if you show the schematic of the single ended and diff output OTAs.

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5. ## Re: Gain bandwidth issue of fully differential amplifier

Originally Posted by sutapanaki
OK, let's get into some details, then. Is your OTA 1 stage or two stage? If it is 2 stages, then your BW is really determined by the miller cap, not the load cap. Load cap only affects the 2nd pole. How about the CMFB? Is it working properly and does it maintain the wanted CM voltage? Maybe it is good if you show the schematic of the single ended and diff output OTAs.
Dear Suta,

I am using folded cacode OTA,

The CMFB is working properly... althaugh I didn't understand the relationship of it to the GBW of the differential amplifier

6. ## Re: Gain bandwidth issue of fully differential amplifier

The GBW does not depend on the CMFB but if the CMFB is not working correctly it can change the operating point of the circuit and thus the GBW and other parameters.

Here is an example single ended and differential folded cascode stages with the same capacitor. See that in the differential one the effective load cap appears 2x higher or equivalently the gm is 2x lower.

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7. ## Re: Gain bandwidth issue of fully differential amplifier

Originally Posted by sutapanaki
The GBW does not depend on the CMFB but if the CMFB is not working correctly it can change the operating point of the circuit and thus the GBW and other parameters.

Here is an example single ended and differential folded cascode stages with the same capacitor. See that in the differential one the effective load cap appears 2x higher or equivalently the gm is 2x lower.

Dear Suta,
That is very useful, I never found this in any text book, can you please provide me a source so I can scientifically write it ?

8. ## Re: Gain bandwidth issue of fully differential amplifier

Oh, that's a problem. I can't provide a source since I just wrote it on a piece of paper and sent it to you. After all it is just common-sense circuit analysis.

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