HeadWize: DIY Workshop > multiloop gain formula (in case anyone is interested)

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DIY Workshop » multiloop gain formula (in case anyone is interested)
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Tophu

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Message [#1] posted on: 02-26-2002 08:43 PM CST (US).

I was doing some work on a multiloop style circuit, and I decided that I needed the equation for the gain of a multiloop style circuit. Since it's a bit more complicated than the normal circuit, I'm sharing the equation just in case anyone else is interested.

With the resistors numbered as in the diagram above, the output voltage is given by:


Vout = Vin * ((R1*(R2+R3+R4)) + (R4*(R2+R3)))
            ----------------------------------------
                (R1*(R2+R3+R4))  +  (R4*R2)

This assumes that U2 is either a unity gain buffer or an opamp configured for unity gain. If anyone wants the formula for U2 with non-unity gain, let me know and I'll sit down and figure it out and post it.

Hope this is useful for someone.

[Edited by Tophu on 02-27-2002 at 01:00 AM.]

transducer

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Message [#2] posted on: 02-27-2002 08:36 AM CST (US).

Hi Tophu,

This is helpful. How would the gain be affected by a series resistor between U1 & U2, as has been suggested here in the past, something about isolating the capacitive input of U2 from U1.

What is the major benefit of using a multiloop gain configuration as opposed to just putting the buffer in the feedback loop of the gain stage?

Thanks,
Transducer

tekir

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Message [#3] posted on: 02-27-2002 12:55 PM CST (US).

A series resistor between u1 and u2 has no effect on gain if it's much smaller than the input impedance of u2 which is very high anyway.
As to the design, I believe this gives u1 better control on the output of u2, and is more stylish <smile>

Cheers

Tophu

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Message [#4] posted on: 02-27-2002 02:13 PM CST (US).

I'll try to explain, but if I get it wrong (its been a few years since my electronics classes, I'm a bit rusty) I hope someone will correct me.

The main difference of the multiloop topology versus simply sticking the buffer inside the feedback loop is that you can control the local gain of U1 separately from the gain of the whole circuit.

One advantage of this is that it lets you take opamps that are unstable at low gains and run them at a relatively high local closed-loop gain, while still having a relatively low overall gain. An example of this would be the OPA637, which is unstable at gains less than 10. Using this circuit you could build an amp with an overall gain of 5, while still keeping the 637 stable.

Also, the interactions of the buffer and the load are somewhat better isolated from the gain of the first stage (because the first stage has its own feedback), which helps with stability.

Joobu

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Message [#5] posted on: 02-28-2002 11:42 PM CST (US).

I don't believe a multi-loop can stabilize local oscillation. That just doesn't make any intuitive sense. First of all, the slower device usually controls the overall gain while the faster device is within the loop. This means if the faster device oscillates locally there is little the loop controller can do if the oscillation is outside of its bandwidth.

The main advantage of multiloop as you stated is the isolation of output with input. If there any non-linearities in the output device, the gain device will de-sensitize the loop.

Tophu

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Message [#6] posted on: 03-04-2002 08:03 PM CST (US).

The part about the multiloop helping touchy opamps was from other sources. After some experimenting, however, I'm beginning to doubt it.

I did some simulating with the 637 (a notoriously touchy beast) and even with local gains around a hundred, if the overall gain was below 10 there was noticeable instability.

I'm beginning to think that the only real benefit is the improved isolation of buffer and gain.

ppl

Headphone Council

Joined: Jul. 28, 2000
Locale: Seattle WA.USA
Total Posts: 1062

Message [#7] posted on: 03-04-2002 11:31 PM CST (US).

Tutchy, i think not if you put a OPA637 in a gain of 20 db and have evean a 30 pf load instability results. Lap a 180 MHz. Buffer within this overall loop and cap load drive goses up to about 100 pf with a critical at 50 Pf for the BUF-634. within a Multi-Loop topology within the Loop of a 180 mhz Buffer has a Phase Margin of about 15 dB this is a far Cry from None and While Still lacking the Perfered Margin for stability, The fact that it is stable justifys the merits of the topology over the more conventional method. I however use more conventional Bandwithth opamps like the AD-825 that gives unity gain stability with speed and Slewing equaling the 637. My new fav opamp for Smooth with Multillop is the AD-8610 this is more stable than evean the Slower OPA-627. My pocket Amp uses a 16 MHz. AD826 in a Multi-Loop Topology with a EL-2001 70 MHz Buffer as per Jungs Artical with Superbe Results and Complete stability into any Cans i have tried.

Moreover while it is true that Multiloop will not stop Local oscilations caused by eather the Gain stage or the Output stage Neather will a Conventional method See Linear tec app note AN=47 http://www.line...app&document=50 for more on this from Jim Willims.While your there check out http://www.line...app&document=23 in addition also see http://www.linea...pp&document=25. I also would like to refer to walts origenal paper discribing the requirement of a linear front end for proper multi-loop operation. in con conclusion, While Multi-Loop canot correct for eather the gain or output stage operating nonlinearly it can and is capable of fully utilizing all the Available Potential of any circuit operating in the Linear range normaly.

[Edited by ppl on 03-05-2002 at 03:56 AM.]

Nicwix

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Total Posts: 145

Message [#8] posted on: 04-29-2002 01:14 PM CST (US).

Tophu

Please could you get your pics working again <smile>

Nic

Tophu

HeadWizer

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Message [#9] posted on: 04-29-2002 09:11 PM CST (US).