# How to simulate the open loop gain of a buffer?

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#### she_long

##### Junior Member level 3
loop gain simulation

Hi all,
I use the normal pmos-input-two stage amp as a buffer, and use Spectre to do the AC analysis. When do the AC analysis, I add the ac signal to Vin+/Vin- like this -> Vin+: AC mag=1 AC phase=180 dc=2.5; Vin-:AC mag=1 AC phase=0 dc=2.5, Vdd=5V, In this condition, I got a AC gain, but the Vout|DC is not 2.5V, I think the output stage isn't in the saturation region. When the amp used as a buffer Vout|DC must be 2.5V, How do I make the Vout|dc=2.5?

A friends advise me that use a large inductor(1GH) and a large cap(1GF) to consist a feedback net to the Vin-, and add the AC signal to the Vin+ only. I've tried it, it worked, Vout|DC=2.5. Is it correct?
Thanks!

#### renwl

open loop gain simulation

yes,it's right.
the inductor provide a dc path for the dc bias.

#### she_long

##### Junior Member level 3
simulate open loop gain

Hi renwl,
Can you explain me more clearly what's the difference between using ind and cap and the direct buffer? and how to decide the ind and cap?
Thanks

#### DenisMark

##### Full Member level 6
middlebrook loop gain

When making DC analysis u obtain buffer configuration of amp due to ind. This helps u to eliminate the influence of offset voltage.
When making AC analysis, ind has large resistance, and capacitor provides ac short. Thus u can simulate open-loop gain.
The value of ind and cap isn't a matter. They must be large enough (e.g. 1H and 1F), so as they don't affect on ac characteristic.

#### RickLi

##### Junior Member level 3
middlebrook method

I used to break the feedback path (from vout to vin-) with a large L (ex. 1GH). vin+ is connected to its DC level, and AC input (mag = 1 and phase = 0) is coupled to vin- with a large C (ex. 1GF). I think this is the definition of the open loop gain.

L should be large enough to be AC open in the frequency range simulated, and C should be large enough to be AC short.

I remember that this method is provided by the book named "The Designer's Guide to SPICE and Spectre (The Designer's Guide Book Series)". But the input capacitance of vin- is not observed by vout, which is a little different from the real case.

Now I seldom use this method. Cadence provides another analysis called STB. Using STB instead of AC is more convenient since no L or C is needed, you only need to use an iprobe or something similar (ex. a 0V vdc) to break the feedback path, and loop gain or phase margin can be plotted directly.

#### bhishma

##### Newbie level 6
middlebrooke loop gain

Refer Roy Choudary and Morris Mano..
The simulation can be done using Multisim..

#### wiedmann

##### Newbie level 3
how to simulate open loop gain

I agree with RickLi. If you are using Spectre, you should use the stb analysis. If you open the loop by inserting an inductor, you might neglect some capacitance and the loop might look more stable than it is in reality.

The stb analysis was developed by Michael Tian and his colleagues from Cadence Design Systems. It is explained in detail in the article <http://www.kenkundert.com/docs/cd2001-01.pdf>. Tian's method is an improved version of Middlebrook's original method (see <http://www.spectrum-soft.com/news/spring97/loopgain.shtm>). It uses the same simulation setup as Middlebrook's method but a different formula to calculate the loop gain. Middlebrook had developed his formula for a loop with no backward transmission. Tian's formula adds forward and backward transmission so that the result is independent of the orientation of the probe. Middlebrook's more recent method for simulating loop gain (see <http://ardem.com/downloads/GFTManual.pdf>) takes backward transmission into account in a slightly different way than Tian. Unlike Tian's method, Middlebrook's method is not symmetrical so that the orientation of the probe does matter in his case.

In order to make Tian's method for simulating loop gain more well-known, I have developed an implementation in LTspice which can be downloaded for free from <http://www.linear.com/designtools/softwareRegistration.jsp>. LTspice is a very good Spice simulator, it is used by the IC designers of Linear Technology Corporation (LTC) for designing their circuits and was originally developed just for this purpose. Some years ago, LTC decided to make it freely available along with models for their ICs in order to help developers in designing circuits with their products. However, LTspice can just as well be used as a general-purpose Spice simulator because it does not have restrictions of any kind. There is a very active and supportive users group on Yahoo at <http://tech.groups.yahoo.com/group/LTspice/> (free registration required) and if one reports a bug to LTC, it is generally fixed immediately.

You can find my implementation of Tian's method for simulating loop gain in the files section of the Yahoo group at <http://tech.groups.yahoo.com/group/LTspice/files/%20Examples/Educational/LoopGain_Probe/>. I recommend that you download the file LoopGain_Probe.zip, which contains all my files in this folder. There are some explanations on the circuit in the thread starting with message 2482 <http://tech.groups.yahoo.com/group/LTspice/message/2482>. The LoopGain2 educational example from the LTspice installation is also using Tian's method. I have made some additional remarks on loop gain simulation in the forum of www.designers-guide.org, for example in <http://www.designers-guide.org/Forum/YaBB.pl?num=1163532257>. You can use the search function of that forum to find additional postings.

#### paley

##### Member level 4
obtainbuffer timed out

use a large inductor(1GH) and a large cap(1GF) to consist a feedback is correct, please see P.E.Allen's book

#### jonashat

##### Member level 4
stb spectre

You might also want to look at the stability analysis (stb) available in Spectre.

I find out the results to be very close to the classical case.

#### boooser

##### Junior Member level 1
loop gain inductor

she_long said:
Hi all,
I use the normal pmos-input-two stage amp as a buffer, and use Spectre to do the AC analysis. When do the AC analysis, I add the ac signal to Vin+/Vin- like this -> Vin+: AC mag=1 AC phase=180 dc=2.5; Vin-:AC mag=1 AC phase=0 dc=2.5, Vdd=5V, In this condition, I got a AC gain, but the Vout|DC is not 2.5V, I think the output stage isn't in the saturation region. When the amp used as a buffer Vout|DC must be 2.5V, How do I make the Vout|dc=2.5?

A friends advise me that use a large inductor(1GH) and a large cap(1GF) to consist a feedback net to the Vin-, and add the AC signal to the Vin+ only. I've tried it, it worked, Vout|DC=2.5. Is it correct?
Thanks!

can you give me a figure about the connection

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