Here is Zin, Zout I get from snap.
Zin is very complicated.

What do you mean by Zin, short compared to Zin, open? What is open and what is shorted?

Same question with respect to Zout. Explain the conditions for the calculation. When you say Zout, open is RD still in place for the calculation of Zout? And, what is shorted or open? Is the input shorted for this?

 

R4 is what determines the input current; without it there would be no input current (other than a parasitic current).

But we do not desire to see any expression for the input current.
As far as I have understood, the current gain is to be calculated.
And a simple visual inspection shows that the input current produces the gate voltage - that`s all. And as long as we have small signal operation the value of the input signal does not influence the gain (neither current nor voltage gain).

What I'm suggesting is that the expression for Ki you got with SAPWIN isn't correct.

Is not correct? May be - I did n`t check it by hand calculation.
However, can you please explain WHY it isn`t correct? Where is the error?
Thank you.

 

But we do not desire to see any expression for the input current.
As far as I have understood, the current gain is to be calculated.
And a simple visual inspection shows that the input current produces the gate voltage - that`s all. And as long as we have small signal operation the value of the input signal does not influence the gain (neither current nor voltage gain).

Yes, the current gain is to be calculated and we need to know the input current to do so. We could apply a known input current, calculate the output current and take the ratio of output to input current to be Ki.

Or, we could apply a known input voltage and calculate the input current as Vin/Zin, using that in the Ki calculation.

Either way, we have to know the input current to calculate Ki, because Ki = Iout/Iin; we need to know both the input current and the output current to calculate Ki.

What I did in post #44 was to apply a known input voltage, Vin, and calculate the input current as Vin/Zin, proceeding from there.

But, if the input current can't be calculated, either because Zin = ∞, or is indeterminate because it is a result of unknown parasitics, then we can't calculate Ki. The presence of R4 gives us a known input impedance, even though the current in it is wasted power, but it is a major determinant of the current gain. As R4 grows larger, Ki also becomes larger.

Is not correct? May be - I did n`t check it by hand calculation.
However, can you please explain WHY it isn`t correct? Where is the error?
Thank you.

We all seem to be agreed that the correct expression for Kv is:

anhnha gets that result in post #38, Jony agrees in post #46, you get this result for Kv in post #55.

I then derive an expression for Ki by the method described in post #44:

I also get this result with a direct analysis using Mathematica.

But, the expression you obtained with SAPWIN, after factoring out and eliminating the extraneous gm2 and R4 factors, becomes:

It's missing an R4 term in the numerator; that is the error I see.

 

What do you mean by Zin, short compared to Zin, open? What is open and what is shorted?

Same question with respect to Zout. Explain the conditions for the calculation. When you say Zout, open is RD still in place for the calculation of Zout? And, what is shorted or open? Is the input shorted for this?

Sorry, I am not familiar with Snap. All expressions are calculated automatically without any equations.

Here is what I get from Snap manual: http://snap.webpark.cz/getting_started.pdf

Therefore, I guess that Zin,open and Zin, short here are input impedances as output is open or shorted respectively.

In the result, Zin, open and Zin, short all contain Rs but no Cgs that seems strange. Zin only contains Rs as Cgs is taken into account, right?

 

Therefore, I guess that Zin,open and Zin, short here are input impedances as output is open or shorted respectively.

In the result, Zin, open and Zin, short all contain Rs but no Cgs that seems strange. Zin only contains Rs as Cgs is taken into account, right?

Notice that your result for Zin, open reduces to simply R4:

The expression for Zin, short should do the same, but doesn't. I wonder why?

 

Yes, the current gain is to be calculated and we need to know the input current to do so. We could apply a known input current, calculate the output current and take the ratio of output to input current to be Ki.

Or, we could apply a known input voltage and calculate the input current as Vin/Zin, using that in the Ki calculation.

It's missing an R4 term in the numerator; that is the error I see.

The Electrician, thank you for explaining to me the meaning of the term "gain". (I suppose, we know each other since a long time, don`t we?)

Yes - you are right, there is a missing R4 term in my current gain expression. But I am happy that SAPWIN is not guilty.
It was a simple typing error in my post#55.
Instead of (R4^2) I wrote just R4. That´s all.
After dividing N and D by gm2*R4 we arrive, of course, at your expression for Vi.
Already a short comparison of the units within D(s) and N(s) could reveal the mistake.
Nevertheless, thank you again for pointing to this typo.

 

Notice that your result for Zin, open reduces to simply R4:

The expression for Zin, short should do the same, but doesn't. I wonder why?

Thanks for introducing the function. I enjoy Mathematica.

I have just tried to simplify and get the same result for Zin, short and Zin, open.

 

The Electrician, thank you for explaining to me the meaning of the term "gain". (I suppose, we know each other since a long time, don`t we?)

Yes - you are right, there is a missing R4 term in my current gain expression. But I am happy that SAPWIN is not guilty.
It was a simple typing error in my post#55.
Instead of (R4^2) I wrote just R4. That´s all.
After dividing N and D by gm2*R4 we arrive, of course, at your expression for Vi.
Already a short comparison of the units within D(s) and N(s) could reveal the mistake.
Nevertheless, thank you again for pointing to this typo.

I must have been prescient in post #57 when I wrote "The current gain numerator would be the same as what I get if the R4 term were R4^2."

I'm not trying to be insulting, LvW, but it seemed to me that you were ignoring my suggestion that there was an error in the expression for Ki you gave in post #55, so in subsequent posts I explained again in more detail.

I couldn't understand why, in post #62, you would ask me where the error was, when in post #57 I had already pointed out the error .

 

Thanks for introducing the function. I enjoy Mathematica.

I have just tried to simplify and get the same result for Zin, short and Zin, open.

You're right; I didn't notice that the Rd term is missing in the denominator of the Zin, short expression.

I expected that should be the result.

Now, I wonder why you didn't get the correct result for Ki in post #38. LvW has already suggested that perhaps you don't have the correct orientation for the VCCS's in your schematic; he gets a correct result for Ki using SAPWIN.

 

Now, I wonder why you didn't get the correct result for Ki in post #38. LvW has already suggested that perhaps you don't have the correct orientation for the VCCS's in your schematic; he gets a correct result for Ki using SAPWIN.

I tried all directions (I think) for current sources and no topology give the right result for current. And the only one in post #38 give the correct for voltage gain.

Here is the description of VCCS in the page: http://snap.webpark.cz/getting_started.pdf

And therefore, I see that both topologies are the same.

 

After reading the manual, I believe this is the correct circuit. However, the current gain still incorrect.
I think this is an error of Snap software.
BTW,

At a frequency that high you definitely need to provide a capacitor to ground from the gate of M2--a capacitor suitable for use at 1.7 GHz!

Could you explain it? Why we need to ground the gate of G2 at high frequency?

 

I think that I know why Snap software gives different result.
It is not a error. The current gain in Snap software is equal to
Ki = (I _outpu_short)/(I_input)
And this is why we don't have Rd in the equation.

After reading the manual, I believe this is the correct circuit. However, the current gain still incorrect.

No, this is not correct circuit. Voltage gain should be negative.
See diagram in post 29.

 

Jony, you are 100% correct.

I tried this circuit to verify your point and get the correct result.

BTW, could you help me understand this?

At a frequency that high you definitely need to provide a capacitor to ground from the gate of M2--a capacitor suitable for use at 1.7 GHz!

 

I'm not a HF guy, so I cannot help. What I know is our small signal analysis is almost worthless at HF.

 

Jony, can you send me the code for Mathematica in the post?
http://forum.allaboutcircuits.com/showpost.php?p=661352&postcount=20

 

Jony, can you send me the code for Mathematica in the post?
http://forum.allaboutcircuits.com/showpost.php?p=661352&postcount=20

Sure, here you have

 

The gate of M2 must be grounded at the frequency of operation. The resistors R1 and R2 will be relatively large in value, maybe many thousands of ohms.

At microwave frequencies, the impedance to ground of the gate of M2 should be much lower so a capacitor is used to ground that gate.

Every capacitor has a self resonance frequency:

http://www.home.agilent.com/upload/cmc_upload/All/exp79.pdf?&cc=US&lc=eng

http://softsolder.com/2011/11/09/self-resonant-frequencies-of-some-ceramic-capacitors/

http://www.cliftonlaboratories.com/self-resonant_frequency_of_inductors.htm

For ordinary capacitors, the SRF (self resonance frequency) will be much lower than 1.7 GHz, so if you try to use an ordinary capacitor, its impedance will not look capacitive at 1.7 GHz. You must use special capacitors that have SRF higher than 1.7 GHz:

http://www.johansontechnology.com/rf-capacitors.html#.UnaIzeKFcYA

 

The gate of M2 must be grounded at the frequency of operation. The resistors R1 and R2 will be relatively large in value, maybe many thousands of ohms.

At microwave frequencies, the impedance to ground of the gate of M2 should be much lower so a capacitor is used to ground that gate.

Sorry, I still don't quite understand.
You said that the gate of M2 must be grounded at high frequency and we can do that by placing a capacitor between gate of M2 and ground.
However, could you explain why we need to ground gate of M2 at high frequency while it is not necessary at low frequency?

 

In case yu are interested:
Here are my simulaton results using SAPWIN:

Voltage gain:
Numerator (N(s)=- gm1*gm2*R4*RD*(R1+R2)

Current gain (through RD):
Numerator N(s)=-gm1*gm2*R4*(R1+R2)

For both cases: denominator

D(s)=gm1*gm2*RS*R4*(R1+R2)+gm2*R4*(RS+RD+R1+R2)

Please note that R4 can be eliminated. This seems to be logical after visual inspection of the circuit.

Consider units!

Voltage gain numerator: units of Ω
Current gain numerator: units of 1
Denominator units: units of Ω + Ω^4

Oops. You KNOW the denominator is wrong. No point going any further until that is fixed.

Furthermore, both voltage gain and current gain are dimensionless, meaning that the numerator has to have the same dimensions as the denominator. This, in turn, means that at least one of the numerators is wrong.

 

Consider units!

Voltage gain numerator: units of Ω
Current gain numerator: units of 1
Denominator units: units of Ω + Ω^4

Oops. You KNOW the denominator is wrong. No point going any further until that is fixed.

Furthermore, both voltage gain and current gain are dimensionless, meaning that the numerator has to have the same dimensions as the denominator. This, in turn, means that at least one of the numerators is wrong.

Denominator units look like Ω + Ω = Ω to me. Did your eyes fool you into thinking that the parenthetical (RS+RD+R1+R2) was (RS*RD*R1*R2)?