Measuring gm for a differential pair

[Ulysses628]

measure gm

Can somebody please tell me how to measure gm for a differential pair in cadence?
Actually the whole circuit is a tunable transconductor but for now I just need to know how to find out
gm versus vin to check linearity. Thanks!

 

[vaibhavar]

constant gm differential voltage

Hi,
You can find gm in Cadence by using following steps:
(1) Perform DCOP analysis, with circuit operating at its bias point.
(2) Then go to results>print>DC operating points and then click on the transistor whose gm you want to check.
(3) You will get operating point values of almost all the parameters (including gm) of that selected transistor.


Good Luck
Vaibhav

 

[Ulysses628]

transconductance value of a differential pair

Oh thanks for the reply but I already know that!

What I am trying to do is to plot gm of the whole circuit versus vin of the
differential pair from -1 to 1 Volt. So my bias voltage is constant and only the
AC varies.. any ideas?

 

[LvW]

simulation setup for transconductor cell

Oh thanks for the reply but I already know that!

What I am trying to do is to plot gm of the whole circuit versus vin of the
differential pair from -1 to 1 Volt. So my bias voltage is constant and only the
AC varies.. any ideas?

I am not familiar with CADENCE, however, there seems to be a general misunderstanding on your side. The parameter gm (transconductance) is constant as determined by the bias condition. It does not vary with any ac signal at the input, unless Vin contains also a dc voltage.

 

[Ulysses628]

diff pair gm analysis

OK, that's totally clear. Of course transconductance has only meaning for DC voltage, but in the
paper I have as a guideline, there are graphs such as: gm versus vin and gm versus i_tune.
The first graph is symmetrical to zero, parallel to vin but curved and distorted.
gm versus itune is like an "S" curve.
My first thought was of course that vin is Vin, I mean a mixed signal. But how 's that possible as we want the input biased?

 

[LvW]

does gm vary with frequency

Perhaps is Vin not the voltage applied at the base/gate of the amplifying transistors but a kind of control voltage at the base/gate of the 3rd transistor in the common "tail" path ?

 

[Ulysses628]

differential pairs graph

no. it is applied in the gates of my pmos differential pair. the nodes of the pair are named
Vcom+vin/2 and Vcom-vin/2 and the plot is gm verus Vin. There is also an Itune that supplies some degeneration transistors that work in triode region, but I dont think that Itune affects the graph becaus is a parameter. There are many curves for a varying itune in the graph.

 

[LvW]

measuring what does gm

It´s a bit confusing. Can you upload the relevamt graph ?

 

[Ulysses628]

differential pair cadence

eh..something like that..

https://obrazki.elektroda.pl/16_1245061724.jpg

Added after 54 seconds:

p.s. different curves for different values of itune

 

[LvW]

differential pair voltage controlled

This doesn´t help too much.
Sorry, but I have asked for a "graph". Instead, I mean: circuit diagram showing all relevant voltages you are speaking of.

 

[Ulysses628]

cadence dc analysis +transconductance

Ok, in google scholar type "soft-switched transconductor" and open the pdf link at the right:
There you can find the paper that I consult, except that mine is with 65nm MOSTs.
I think that the graph we were talking about is DC sweep but I have many problems with linearities yet!
I have no idea what Itune have to use yet and time is running!

Thanks for the concern any advice would be helpful and I 'd be greatfull

 

[LvW]

transistor gm value around

OK, I had a short look into the paper.
Now it´s clear for me why the term called "transconductance" is connected with the input voltage. It is not the transconductance of an amplifying transistor but the transconductance of the whole circuit, because:
The whole arrangement is a voltage-to-current converter (i. e. the output signal is a current!). In this case it is clear that the ratio output-to-input is a transconductance and, of course, depends on the input voltage.
As far as the tuning current is concerned, I think it is something like a bias current establishing the basis for operation and determining the transconductance niveau of the whole circuit - that means: Itune determines if the transconductance, for example, is in the milli- or mikro-range.

 

[sutapanaki]

transconductance parameter

When I have to measure trans-conductance of an OTA I usually do it in AC. I connect big capacitors of may be 1F at the outputs and the other ends of the capacitors go to a 0v voltage source. I measure the AC current through this source wrt the input AC voltage. The capacitors help to preserve undisturbed the biasing of the cell. The current that I measure this way is only the output current i.e. it does not include the current that gets diverted into the parasitics of the OTA itself. This way I can see the DC value of the Gm and its frequency behavior.

 

[Ulysses628]

differential pair

...but dear Sutapanaki is measuring AC output current wrt AC input voltage concidered transconductance? I think transconductance refers to DC behaviour only.
For my measurements I 've put a port (cadence item that takes any value of resistance, capacitance etc) of 200K . Do I have to put capacitance also?
As for the graph of transconductance, my professor told me to perform DC sweep wrt bias current to see which area is linear.

 

[sutapanaki]

measuring differential pairs

We can agree that the trans-conductance is deltaI/deltaV where deltaI is the output current change of the cell. This ratio of deltas can be done at DC and you'll get the DC value of the transconductance. AC analysis is doing just that - it linearizes the circuit around an operating point, applies some input voltage increment and produces output current increment. If you do the AC analysis at sufficiently low frequency this will be effectively DC. Another way you can do it is to do DC analysis, apply delta V at input and see what delta I it produces at the output. I personally like AC because OTAs very seldom are used at DC only. Most often than not they are used in frequency domain, so I like to see how does the trans-conductance change with frequency, that is to say how does the current going into the load change with frequency for a constant deltaV at the input.
Putting big capacitors at the output and a 0v voltage source makes sure that your output current is going into an AC short which is the proper way to measure current of a current source. And it doesn't disturb the biasing of the OTA.
Changing the bias current, as your professor asked you to do will produce different trunsconductance values. You could then extract the value of the trunsconductance at DC and plot it against the bias current to see how it depends on the biasing. You should be able to do this in Cadence, I don't know exactly how, I'm using a different kind of simulator.

 

[Ulysses628]

measure rout

thank you for your advice both! The paper says that the circuit was dimensioned for a tuning range of a factor two. What does this mean? My Ibias (2Io) is 4uA. Does this mean that I shall have a constant value for Itune around 2uA?

 

[sutapanaki]

gm of differential pair vs single transistor

Without reading the paper, I would assume that a tuning range of 2 means your cell transconductance can change 2 times in response to the tuning control. If it is used in a filter, then this could be that you tune your frequency 1:2.

 

[foveacentralis]

gm measuring circuit

The way to measure gm of a OTA in cadence, or any simulator, is as follows:
Set up an open loop transient sim.
Bias the reference(non-inverting) input of the OTA to the desired value (Ref).
Add a resistor at the output node to ground (Rout). Monitor the current flowing into the resistor.
Do a transient sweep of the other(inverting) input of the OTA from Ref-X,mV to Ref+X,mV.
Gm, transconductance of the circuit is defined as Δiout/Δvin.
Measure the current flowing into the output resistor(i1) when vin1=Ref-X,mV and the current flowing into the output resistor(i2) when vin2=Ref+x,mV,
Now gm is given by Δiout / ΔVin = (i1-i2)/(vin1-vin2).
You can choose the value of X and R so the output voltage does not run into head room issues either near VDD or GND, depending on the value of the gm that the circuit is designed for. If gm is small you can use big values of X and vice versa. Typically values like 1 to 2mV for X and 1K for Rout would work.
It doesnt have to be transient, you can do 2 DC sims, one with Ref-X,mV and another with Ref+XmV on the inverting input, collect the output current data on both cases and use the same equation.

 

[Ulysses628]

how to find gm of a circuit

thank you all so much!
What I have done finally is measure Iout versus Vin and then taking the derivative of the curve. Vin is vbias -vdc/2 for the one input and vbias +vdc/2 for the other. so I do a DC sweep and take an "S" like curve. any ideas how to increase the linear area, so as to take more constant gm?

have a nice day!