Calculating loop gain and phase in multisim

[ajfaul]

I am trying to simulate loop gain and phase for an oscillator in multisim.  I use the Middlebrook method and can get the current gain and voltage gain using the "add expression" feature in the analysis.  I then need to use these gains to calculate the loop gain and phase using the equation T = ((Ti*Tv)-1)/(Ti+Tv+2), where Ti and Tv are the current and voltage gains respectively.  I have been unable to implement the last expression and will appreciate any help.

Thanks

Andre 

[_user32 · Accepted solution]

Andre,

Yes the Middlebrook analysis technique can be implemented with Multisim.   Please see the circuit below as an example on how to implement this method within Multisim.

Let me know if you have any questions.

Regards,

Pat Noonan

National Instruments

[ajfaul]

Thanks Pat.  Your example helped a lot.

[ares1]

hi,

using you example and merging it with "LabVIEW Multisim Connectivity Toolkit" i create this simple programm to help gloop simulation. In my example you have just to add a gloop_block and 3 variants in your desing, without having different copies of circuit.

Using a labview code I do different simulations and evaluate the loop gain with Middlebrook method. Is possible have parametric simulation of gloop.

hope it's useful

nicola 

[ares1]

sorry, forgot subvi

[_user32]

ares1,

Thank you very much for the inclusion of this example.   I will try it out and compare with traditional Middlebrook technique using expressions in analyses on some other circuits that I have.

Good contribution...

Regards,

Pat Noonan

National Instruments

[Jenyok]

Calculating loop gain and phase in Multisim
This is Tian's Method to calculate loop gain and phase

.

See attached files.
"Tian_s_Loop_Gain_test.ms14"
"Tian's Method.png"
"gain_and_phase.jpeg"
"Simmy_Loop.gif"
"gtnkt.jpg"

.

Statements

1. There is NO additional NI and other companies programs, ONLY pure Multisim. For example, do NOT use NI LABView and so on.
2. Multisim Grapher View is used to see AC Sweep loop gain and phase. But there is only ONE field to display two superimposed graphs in Multisim Grapher View, as DC Sweep Grapher View is.
3. X axis is frequency. Y axis (LEFT) is magnitude in db, Y axis (RIGHT) is phase in degrees.
4. Two graphs (magnnitude vs frequency and phase vs frequency) are displayed in ONE field Multisim Grapher View. See attached pic files. For example "gtnkt.jpg" .

.
The main task in the development and designer of ultra linear high power amplifiers is that the amplifier is
designed so that the phase margin is at least 45° and power amplifier also has a maximum gain at a frequency
of 20 kHz when plotting graphs the (open) loop gain and phase.

.

Your сompetitors in simulation Software such as MicroCap, LTC Linear Technology do it
(calculate and plot graphs loop gain and phase) well.
Microcap 9 (!!! OLD version) does it (calculate and plot graphs loop gain and phase) in one command.
LTC Linear Technology does it (calculate and plot graphs loop gain and phase) in 3 - 4 simulation
directives at circuit.

.
It is very strange, that well publicized simulation software NI Multisim does not know how to do this
(calculate and plot graphs (open) loop gain and phase) !!!

.

Attached file: "gain_and_phase.jpeg"

The first cursor marks the amplitude (gain) where it crosses the 0 dB line and the second cursor marks the
amplitude (gain) where the phase shift is 180°. The gain margin is the difference (expressed as a positive value in dB)
between 0 dB and |A?| at f180 . A greater margin of reinforcement means more resilience. Similarly, the phase
margin is the difference (expressed as a positive number) between 180° and the phase shift where the |A?|
crosses the 0 dB line. If it's still a little confusing, look (thoughtfully) at the graph above a little bit more.
The most commonly used metric is phase margin, perhaps because it has a convenient rule of thumb:
the power amplifier must be designed so that the phase margin is at least 45° . A greater phase margin means
greater stability amplifier, because a higher phase margin indicates that the frequency at which the magnitude
of the (open) loop gain reaches unity is further from the frequency of the terrible 180° phase shift turning
negative feedback into positive.

.

I think that simulation of loop gain and phase is NOT correct, because there are NO @1 - step1 and @2 - step2
in calculation loop gain and phase.

.

Question.

How is implemented calculating loop gain and phase in pure Multisim according statements, see upper ?

.

Http links are

https://www.edaboard.com/threads/middlebrooks-method-vs-tians-method-vs-middlebrooks-general-feedbac...
https://www.spectrum-soft.com/news/spring2011/loopgain.shtm
https://www.spectrum-soft.com/news/fall2013/stability_analysis.shtm

.

Formula to calculate (equation for computation) loop gain and phase is shown in attached pic file.

.
-1/(1 -1 / (2 * (I(Vi)@1 * V(x)@2 - V(x)@1 * I(Vi)@2) + V(x)@1 + I(Vi)@2))

@1 - step 1
@2 - step 2

Vi AC{u{-prb}}
Ii AC{u{prb}}

step param prb list -1 1

Vi AC{u{1}} @1
Vi AC{u{-1}} @2

Ii AC{u{-1}} @1
Ii AC{u{1}} @2

.

[Jenyok]

Attached files.

.

[Jenyok]

Calculating loop gain and phase in Multisim
This is Tian's Method to calculate loop gain and phase

.

See attached files.
"Tian_s_Loop_Gain_test.ms14"
"Tian's Method.png"
"gain_and_phase.jpeg"
"Simmy_Loop.gif"
"gtnkt.jpg"

.

Statements

1. There is NO additional NI and other companies programs, ONLY pure Multisim. For example, do NOT use NI LABView and so on.
2. Multisim Grapher View is used to see AC Sweep loop gain and phase. But there is only ONE field to display two superimposed graphs in Multisim Grapher View, as DC Sweep Grapher View is.
3. X axis is frequency. Y axis (LEFT) is magnitude in db, Y axis (RIGHT) is phase in degrees.
4. Two graphs (magnnitude vs frequency and phase vs frequency) are displayed in ONE field Multisim Grapher View. See attached pic files. For example "gtnkt.jpg".

.
The main task in the development and designer of ultra linear high power amplifiers is that the amplifier is
designed so that the phase margin is at least 45° and power amplifier also has a maximum gain at a frequency
of 20 kHz when plotting graphs the (open) loop gain and phase.

.

Your сompetitors in simulation Software such as MicroCap, LTC Linear Technology do it
(calculate and plot graphs loop gain and phase) well.
Microcap 9 (!!! OLD version) does it (calculate and plot graphs loop gain and phase) in one command.
LTC Linear Technology does it (calculate and plot graphs loop gain and phase) in 3 - 4 simulation
directives at circuit.

.
It is very strange, that well publicized simulation software NI Multisim does not know how to do this
(calculate and plot graphs (open) loop gain and phase) !!!

.
See attached file "gain_and_phase.jpeg".
The first cursor marks the amplitude (gain) where it crosses the 0 dB line and the second cursor marks the
amplitude (gain) where the phase shift is 180°. The gain margin is the difference (expressed as a positive value in dB)
between 0 dB and |A?| at f180 . A greater margin of reinforcement means more resilience. Similarly, the phase
margin is the difference (expressed as a positive number) between 180° and the phase shift where the |A?|
crosses the 0 dB line. If it's still a little confusing, look (thoughtfully) at the graph above a little bit more.
The most commonly used metric is phase margin, perhaps because it has a convenient rule of thumb:
the power amplifier must be designed so that the phase margin is at least 45° . A greater phase margin means
greater stability amplifier, because a higher phase margin indicates that the frequency at which the magnitude
of the (open) loop gain reaches unity is further from the frequency of the terrible 180° phase shift turning
negative feedback into positive.

.

See attached file "Tian_s_Loop_Gain_test.ms14".

I think that simulation of loop gain and phase is NOT correct, because there are NO @1 - step1 and @2 - step2
in calculation loop gain and phase.

.

Question.

How is implemented calculating loop gain and phase in pure Multisim according statements, see upper ?

.

Http links are

https://www.edaboard.com/threads/middlebrooks-method-vs-tians-method-vs-middlebrooks-general-feedbac...
https://www.spectrum-soft.com/news/spring2011/loopgain.shtm
https://www.spectrum-soft.com/news/fall2013/stability_analysis.shtm

.

Formula to calculate (equation for computation) loop gain and phase is shown in attached pic file.

.
-1/(1 -1 / (2 * (I(Vi)@1 * V(x)@2 - V(x)@1 * I(Vi)@2) + V(x)@1 + I(Vi)@2))

@1 - step 1
@2 - step 2

Vi AC{u{-prb}}
Ii AC{u{prb}}

step param prb list -1 1

Vi AC{u{1}} @1
Vi AC{u{-1}} @2

Ii AC{u{-1}} @1
Ii AC{u{1}} @2

.

[Jenyok]

Specification in previous post.
.
|A?| = |Aβ|

where
A - open loop gain of amplifier
β (beta) - negative feedback of amplifier
.
See attached files.
.