Calculating open loop gain using LTSpice

[dadod]

With big inductor you will get Open Loop Gain, with Tian, Middlebrook and AC1 source you will get Loop Gain (OLG minus amp Gain).

 

[joensd]

Thanks a heap guys. I see there´s lots to digest.

 

[jan.didden]

With big inductor you will get Open Loop Gain, with Tian, Middlebrook and AC1 source you will get Loop Gain (OLG minus amp Gain).

I think that is incorrect. If you break the loop in a feedback amp, by whatever means, you measure the loop gain, by definition.
You 'go around the loop' and measure the gain.

Again, big inductor has nothing to do with the method by which you measure. It is a band aid to maintain DC conditions.

Jan

 

[Bonsai]

For plotting OLG, I insert a 1^12 H inductor in series with the feedback resistor. This provides th3 input stag3 with th3 needed DC deer back, so it converges without problems and you get a near enough accurate handle on OLG.

I’ve used the Tian probe for loop gain but for general audio work have found it’s not much more accurate than just inserting an AC source in series with the feedback resistor (output side of the amp) and then plotting Vo/Vx where Vx is the other side of the voltage source.

(Caveat: My feedback resistor networks are low impedance (15 to 33 ohms for Rg and 300 to 1k for the feedback resistor) because the amps are CFA so the network loading issues aren’t as critical as in deigns using more conventional higher values.)

 

[KSTR]

@Jan,
Dadod is correct.
Tian measures loop gain and phase at the actual noise gain dialed in, therefore good for stability analysis. For small and constant noise gains open loop gain/phase and loop gain/phase reserve often look close to identical on a large scale plot...

 

[dadod]

I’ve used the Tian probe for loop gain but for general audio work have found it’s not much more accurate than just inserting an AC source in series with the feedback resistor (output side of the amp) and then plotting Vo/Vx where Vx is the other side of the voltage source.

(Caveat: My feedback resistor networks are low impedance (15 to 33 ohms for Rg and 300 to 1k for the feedback resistor) because the amps are CFA so the network loading issues aren’t as critical as in deigns using more conventional higher values.)

I think it's opposite, for low impedance FB network better to use Tian.

 

[joensd]

For plotting OLG, I insert a 1^12 H inductor in series with the feedback resistor.

I know this has been discussed before and people mix it up
but OLG is "open loop gain" and doesn´t the name already suggest that this is the gain WITHOUT feedback?

 

[Bonsai]

It effectively is ‘without feedback’ at AC because the inductor Z is >> greater than the feedback resistor even at LF

 

[Bonsai]

I think it's opposite, for low impedance FB network better to use Tian.

I’m not getting any real differences between the two dadod. I think the Zin on the CFA’s is pretty flat and wideband, but maybe you have a different experience. I’ve never had compensation stability issues on any designs optimized in LTSpice (parasitics yes! But that is different). Your designs have much higher loop gains, so it might be you see a difference between Tian and a straight Vo/Vx plot.

🙂

 

[joensd]

It effectively is ‘without feedback’ at AC because the inductor Z is >> greater than the feedback resistor even at LF

Thanks Bonsai

 

[jan.didden]

@Jan,
Dadod is correct.
Tian measures loop gain and phase at the actual noise gain dialed in, therefore good for stability analysis. For small and constant noise gains open loop gain/phase and loop gain/phase reserve often look close to identical on a large scale plot...

Really? OK, learned something again. It never stops ;-)

Jan

 

[Bonsai]

I think if you are designing systems where phase margin is taking a back seat to overshoot optimization (high speed DAC for example, or video amps) then you must use Tian. Small PM differences will have a big effect because usually the available PM is small. In these types of applications, the load impedance is well defined and does not change over the life of the product ie it’s fixed so you can push the envelope.

On audio power amps this is not the case as the load conditions cover a wide range so, you should aim for 60+ degree PM and gain margins of 10+ dB. Even with a worst case reactive load, you still have tens of degrees PM and +6 dB GM. In this case I found a straight Vo/Vx plot is sufficient. YMMV.

 

[dadod]

I’m not getting any real differences between the two dadod. I think the Zin on the CFA’s is pretty flat and wideband, but maybe you have a different experience. I’ve never had compensation stability issues on any designs optimized in LTSpice (parasitics yes! But that is different). Your designs have much higher loop gains, so it might be you see a difference between Tian and a straight Vo/Vx plot.

🙂

Yes, I agree, no big difference. But way not use Tian if it's so simple to use?😉

 

[Bonsai]

Maybe I should 🙂

 

[edbarx]

Thanks for all your replies. I searched online to find websites describing the Tian Test/Probe method and failed to find anything helpful. I only found scattered and fragmented information. Together with that, when I found a webpage explaining how to do a Tian Probe, the webpage information was outdated by two decades. It made references to dialog boxes and dialog options which no longer exist in LTSpice. Furthermore, the graphics describing what pseudo-components should be added, were inaccessible. This left too many gaps in the method, and I ended up not being able to do any Tian Tests. So, I reverted back to what I was doing.

The Method:
To calculate the open loop gain I devided the amplifier in two parts which isolated the input stage and the part from the VAS onwards. The negative feedback loop was broken.

The first thing to do was to simulate the amplifier with the negative feedback loop closed. This was done to find the minimum and maximum current fed in the VAS's input.
Injecting a current into the base of the VAS using a current source with a DC current of 35uA and AC signal with a peak of 65uA, the output swing of the VAS was about 100V. These values yield the following calculation:

VAS dV/dI = (30 - (-70))/(100e-6 - (-30e-6))
          = 769231 Volts/Amperes

After this, the input stage was fed a voltage of 20mV peak superposed on 10mV DC. This allowed the voltage to remain always positive (Yes, Zero is defined as positive). The output from input stage was directed into two signal diodes in series connected to the positive voltage rail that drives the input stage and VAS. The current through these latter diodes was plotted together with the differential input voltage into the bases of the differential pair. The following is a calculation with this data:

dI/dV = (250e-6 - 647e-6)/(9.82e-3 - 23.77e-3)
      = 0.0285 Amperes/Volt

Knowing the input stage's gain (Transconductance, although it has nothing to do with conductance), the open loop gain at 2000Hz was calculated by multiplying the two gains, as follows:

open loop gain = input_stages_transconductance * VAS_transresistance
                         = 0.0285*769231
                         = 21923

All calculated gains are RAW gains.

This second calculation corroborated my first findings.

 

[joensd]

I searched online to find websites describing the Tian Test/Probe method and failed to find anything helpful.

There is an example in the LTspice folder examples/educational (the Tian probe is in the file LoopGain2.asc).
Here´s an article from Tian&Co that might help:
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwje2u20utXvAhWJlqQKHd3DAl8QFjAAegQIAxAD&url=https%3A%2F%2Fkenkundert.com%2Fdocs%2Fcd2001-01.pdf&usg=AOvVaw0nOyfB0sz8Je0MQv4xG7jD

 

[spladski]

Instructions added

 

[edbarx]

Thanks for replying. Finally, I could execute the test. The provided example calculated some form of power as the expression for the graph involves products of voltage and current. Seeing the thus obtained results, I had to change the expression for the graph with V(output)/(V(a) - V(b)), where a and b are the non-inverting and inverting inputs respectively. The results obtained, corroborate my previous calculation results, and the shape of the open loop gain is typical of commercial opamps. This is a further corrobate that what I am doing should be in the right direction. The open loop gain for my giant opamp is extremely high for very low frequencies dropping to about 3300 times at 16kHz. It has the form of a single step with the high end at low frequencies and the low end at high frequencies. It is composed of three distinct linear segments.

Considering a raw gain of about 60 with negative feedback, this is enough. In fact, the amplifier works and is used every day.

I am attaching a screenshot.

 

[jan.didden]

Ed did you find this:

Loop Gain Simulation - Frank Wiedmann

Jan

 

[triode_al]

Interesting, but very complex for a simple mind . . .

• I saw a Spice simulation, where there was a simple math. It used the expression 'gain', and this Gain was used in a plotted expression.

But of course I cannot find sich a formula or expression for 'Gain'.
Any hint?
It is for analysing a simple one element closed-loop stage 1) with NFB to the input (anode to grid) and optionally, and 2) some other small PFB to the cathode. I want to use it to show the distortion phase in the output.