phase margin with input AC current stimulus

Is there any trick in AC analysis to find the phase margin if the input stimulus is AC current instead of the AC voltage. If the input is AC current, the magnitude response is impedance rather than the intuitive voltage ratio. It seems like the PM in stability criterion does not apply any more for input AC current stimulus. Any idea how to judge the stability in AC analysis if input stimulus is current?

The trick is to determine the input impedance and apply Thévenin's theorem.

If it is nonlinear, then piece wise linear approximations might work at different levels.

If polarized current, then both directions could be analyzed with AC superimposed and might get tricky.

I think current gain analysis with feedback would have the same requirement of unity gain , phase margin.


Even an emitter follower can oscillate with a capacitive load and base inductance leads to the over unity gain with sufficient Q to resonate if the gain is over unity between the range of fT and fT/hFE.


The same logic applies to current sources with capacitive loads and inductive feedback and Bode Plots can be doe for current gain just as in voltage gain.

Thank you, SunnySkyguy. I guess if I just plot the magnitude of current through the interested source or drain nodes of transistors, PM criterion should work. Sinewave of current delayed by 180 deg. with current gain equal to 1 should augment itself and oscillate. I can try it to check if PM criterion is the same for both voltage gain and current gain.

Vanderpollator said:

Is there any trick in AC analysis to find the phase margin if the input stimulus is AC current instead of the AC voltage. If the input is AC current, the magnitude response is impedance rather than the intuitive voltage ratio. It seems like the PM in stability criterion does not apply any more for input AC current stimulus. Any idea how to judge the stability in AC analysis if input stimulus is current?

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I think, the answer simply is: It depends on the kind of feedback.
In case of voltage feedback (example: opamp based circuits) we must use a voltage stimulus and in case of current feedback we must use an ac current stimulus.
However, in reality we have both at the same time (because nothing is ideal) - but in most cases one of both is dominating.
We only must remember Middlebrook´s "Two-injection method". This method for correct loop gain simulation requires two ac analysis - one with voltage and one with current injection.
Then, the real loop gain can be found using a special formula for combining both results.

Perhaps, I should add for clarification: Speaking about "loop gain" we should be aware that in REAL circuits (input/output resistances are never zero or infinite) we always have two classes of loop gain:
Voltage loop gain and current loop gain.
And the relevant loop gain for stability analysis can be found based on Middlebrook´s method, but in many cases single injection (voltage or current) is exact enough.

Thank you, LvW. I am confused now. I only know a smattering of Middlebrook's method. But I thought it is just to do AC analysis without breaking the feedback path. However, in Cadence Spectre, I can use a special Cadence element and it will connect the feedback path in DC and automatically break the feedback path in AC. My input stimulus must be current since it is a sharp photo-current variation. I am still puzzled how to handle my circuit since if I plot mag(v(---)) it is just impedance and if I plot mag(i(---)), the current ratio turns out to be unity or less than unity, rendering PM criterion useless.

Vanderpollator - I am not familiar with Spectre and it´s stability check.
However, the loop gain must be either V/V or I/I (that means dimensionless).
A reliable indication that the stability crierion cannot be applied (because of a "false" loop gain) is a phase shift other than -180 deg at low frequencies (including dc).
My sugestion:
Look for a node within the loop where
* a small ac source impedance works upon a much larger ac load impedance (voltage injection), or
* a large ac source impedance works upon a much smaller ac load impedance (current injection).

When such a node cannot be identified you must use Middlebrook´s two-injection method for combining both ac simulations results.

Lvw, thanks again. I may just wrap up this discussion since I start to believe my circuit conundrum may be due to other unexpected events rather than oscillation. As for your useful comments, unfortunately, I still don't grasp the essential advantages of Middlebrook's method. In the last few years for AC analysis, I feel very comfortable for either of the following methods: 1) using Cadence's "DC-on AC-off" special element to have one-shot AC analysis or 2) If without Cadence special element, then, do the closed-loop DC analysis followed by open-loop AC analysis by placing, e.g., a voltage source on the broken feedback node with at least 6-digit (or even 8-digit if open-loop gain is enormous) accuracy. Both methodologies work perfectly for me in the last few years.

Some of the peoples simulating stability of transimpedance amplifiers using following schematics:

The feedback signall is out_ac node, it is a voltage drop on a one Ohm resistor R7.

Dominik Przyborowski said:

Some of the peoples simulating stability of transimpedance amplifiers using following schematics:

The feedback signall is out_ac node, it is a voltage drop on a one Ohm resistor R7.

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Dominik, your crcuit diagram is hard to read. Please, can you describe the method with words (if it differs from the established methods)?

This is circuit diagram is for classic breaking loop analysis and I think it's described in Hurst paper about breaking the loop for different feedback types (that one from IEEE Tran. on Cir. and Systems I from 1991). But I have to admit that I'm only copy-paste it from one old wise guy, whose learn it from other, older and wiser one many years ago ;-)

In fact to ac analysis only the two right amplifiers are used, the V1 vdc source only sensing input leakage current for F0 cccs (it's necessary for transimpedance amplifiers due to quite large area of input transistor). E1 vcvs provides correct OP for replica amp with broken loop and the feedback current is sensing on 1Ohm R7 resistor.


//edit:
Backing to main thread problem. Maybe pole-zero simulation and on hand calculation of stability using Ruth-Hurwitz method could be a good solution?

Spectre uses Tian method for stability analysis. The method is completely independent of the type of stimulus you use as it simply calculates the return ratio of the loop or can actually detect instability when the feedback loop is within a single device (e.g. emitter follower instability).
Have a look at spectre manual for details.
Cutting the loop during AC analysis is not accurate and it can lead to nasty surprises with some circuit topologies. Two things will be altered feedforward gain (often negligible) and input loading on the feedback (often not negligible).

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dgnani said:

Spectre uses Tian method for stability analysis.
...............
Cutting the loop during AC analysis is not accurate and it can lead to nasty surprises with some circuit topologies.

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I know Tian´s method. However, introducing a series voltage source into the loop is a kind of "cutting", it is not?
And - I think - exactly this is the reason for using additional current injection (for error compensation).

- - - Updated - - -

Vanderpollator said:

Any idea how to judge the stability in AC analysis if input stimulus is current?

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There is something coming just into my mind: There is another method with current injection called "non-invasive" phase margin determination.
In this method, an ac stimulus is injected into the output node of a closed-loop system with the aim to get the output resistance as a function of frequency.
This function will exhibit something like a resonant peak around the frequency where the loop gain is unity. Determining the Q value of this peak (3dB points) allows calculation of the phase margin using a special formula.
I have used this method - in comparison to established methods - and it works good and exact!

Hi LvW

Tian's method does indeed include a double injection (current+voltage) as the older Middlebrook method (1976) [but it is more complete than Middlebrook's old method as it consider bilateral blocks to accounts for feedforward, in response Middlebrook came up with a new method accounting for feedforward but that's a whole other story - somewhat messier, I would say, but definitely illuminating as of why there are so many contrasting opinions on this subject] but spectre implementation requires only one 0V source inserted anywhere all feedback loops are 'broken' at once (if at all possible). Double injection is performed under the hood...
The 0V source does not disturb the AC analysis in any way, and the loading and/or feedforward effects are still simulated correctly.
Spectre also allows in alternative to identify a device and one of its internal components and evaluate their stability (this was part of Tian's original article as well)

If you have a reference for the "non-invasive" phase margin determination, I'd be very interested.

P.S. Good luck to Germany in today's game, tschüß

dgnani said:

If you have a reference for the "non-invasive" phase margin determination, I'd be very interested.

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**broken link removed**

PS: I have found another (novel) method for exact phase and/or gain margin determination by introducing some additional phase shift into the loop. Please, give notice if you are interested.

dgnani said:

P.S. Good luck to Germany in today's game, tschüß

Click to expand...

Thank you. Yes - we had some luck. But there are some events in our world which deserve more attention.

Hi LvW

Thanks for the link, I skimmed through it but I cannot tell under what assumption this works. I'll ask if you've had some experience with it.
I am always interested in new stability criteria... Let's call it an hobby. Feel free to post here or privately if you feel it is off topic.

As of soccer/football, congrats and yes I find it tolerable to look into it every four years