Relationship of Z11, ZM and ZP in calculating input impedance

[sharethewell]

I used S parameter analysis in Cadence to measure input impedance of an RF power amplifier working at 433MHz. From sp analysis, it plots Z11 contour on smith chart.

Here is my question:
Can I say input impedance of my PA is equal to 50(ohms) times Z11?

Or is there another equation to calculate input impedance? What is it?

Thank you.

 

[prcken]

Re: Z11=input impedance?

i just know that
Vin=Z11*Iin + Z12*Iout
so that
Z11=Vin/Iin when Iout=0

 

[sharethewell]

Re: Z11=input impedance?

i just know that
Vin=Z11*Iin + Z12*Iout
so that
Z11=Vin/Iin when Iout=0

Thanks. Are you familiar with Cadence SP analysis? I am trying to plot input impedance. Do you know how to do that?

 

[prcken]

Re: Z11=input impedance?

i am not quite familiar, i think just plot S11 in smith chart to see whether it's matched or not.
for Z11 i think it's a complex value, the real part of Z11 is the input resistance, i think you can plot the value versus frequency

 

[flatulent]

Re: Z11=input impedance?

If z12 is not zero, the input impedance will be different from Z11 if you have a load that is not a short circuit. Usually Z12 is so small that there is little difference for practical purposes between input impedance and z11 unless you are using the active device near the high frequency end of its range.

 

[sharethewell]

Re: Z11=input impedance?

i am not quite familiar, i think just plot S11 in smith chart to see whether it's matched or not.
for Z11 i think it's a complex value, the real part of Z11 is the input resistance, i think you can plot the value versus frequency

I see. Thank you. I am designing a RF PA. I measured the input impedance of the driver stage of my PA without adding impedance transformation network by using ZM1 of SP analysis. The strange thing is that the input impedance is negative. I don't know if that's the way it is before it is matched up to 50 ohms, or because the drain of the transistor is connected to 2 parallel LC resonant network(one should be tuned at fundamental frequency, the other is at the third harmonic)?


Here is a circuit that has the same driver stage as mine using class F PA. Any idea why it is negative? Or what may cause it to be negative?
**broken link removed**

---------- Post added at 02:17 ---------- Previous post was at 02:04 ----------

If z12 is not zero, the input impedance will be different from Z11 if you have a load that is not a short circuit. Usually Z12 is so small that there is little difference for practical purposes between input impedance and z11 unless you are using the active device near the high frequency end of its range.

Now I use ZM1 of SP analysis to measure input impedance of my PA driver stage without adding input impedance transformation network. It should be accurate right?

However, I got a negative value for real part of ZM1! Any idea? I was told it is oscillating. I don't know how to check it is oscillating. Also this power amplifier works in nonlinear region on purpose. Don't now what went wrong. I am trying to figure out what causes it to be negative. Please refer to the circuit in the picture above. Thanks!

 

[prcken]

Re: Z11=input impedance?

sorry, i have no experience about that.
but curious about it, seen from the right of Lg1 to the input of the NMOS, it's the gate of MOS and loaded with a 10K bias resistor, i think the real part should be almost 10Kohm.
anyway, what does ZM mean, i never used it.
i think you can also use ZP and check the real part of Z11 instead and see whether it is still negative?

 

[sharethewell]

Re: Z11=input impedance?

sorry, i have no experience about that.
but curious about it, seen from the right of Lg1 to the input of the NMOS, it's the gate of MOS and loaded with a 10K bias resistor, i think the real part should be almost 10Kohm.
anyway, what does ZM mean, i never used it.
i think you can also use ZP and check the real part of Z11 instead and see whether it is still negative?

Thanks. I tried ZP. The real part is negative (-123.6) as well. Don't know what went wrong. I did this when the Cb and Lg1 are removed so that not impedance matching network is in it.

Why do you think the real part is about 10K ohms? What if the biasing resistor is placed in parallel with capacitive impedance (Cgs). Since Rg1 is far greater than the capacitive impedance, then 10K should have very little affect on over all impedance. right?

I just found out that ZM1 is used to measure input impedance. It is in function section of main forms.

So any idea?

 

[prcken]

Re: Z11=input impedance?

Why do you think the real part is about 10K ohms? What if the biasing resistor is placed in parallel with capacitive impedance (Cgs). Since Rg1 is far greater than the capacitive impedance, then 10K should have very little affect on over all impedance. right?

yes, the 10K ohms resistor can be ignored since there is a much smaller impedance in parallel.
i have no idea now. hehe

 

[sharethewell]

Re: Z11=input impedance?

yes, the 10K ohms resistor can be ignored since there is a much smaller impedance in parallel.
i have no idea now. hehe

By the way, what is ZP? How different is it from S11 of SP and ZM1 of SP? Using ZM1, the input Impedance(real part) of my output stage is negative. However, using ZP, the real part is positive. That's strange! Do you know what's the difference between them? Could you give me more details?

By the way, I found out that I may measure the input impedance of the driver stage in a wrong way. Once I disconnected output stage from driver stage and tested the driver stage individually I found that the input impedance became positive! Amazing! Don't know why. But it happens!

Thank you very much!

 

[BigBoss]

Re: Z11=input impedance?

ZPort Impedance.Whe you look through a port, the impedance which you'll see from this port.
ZM:Open circuited Z parameter.It's totally different than ZP because Z12 is not zero.The impedance which you will measure with VNA will be ZP, NOT ZM.
But they are convertible between them.

 

[sharethewell]

Re: Z11=input impedance?

ZPort Impedance.Whe you look through a port, the impedance which you'll see from this port.
ZM:Open circuited Z parameter.It's totally different than ZP because Z12 is not zero.The impedance which you will measure with VNA will be ZP, NOT ZM.
But they are convertible between them.

Thanks. What is VNA? I just set up my circuit like: port1+circuit+port2

Does it mean ZP is more accurate than ZM1 if my circuit is set up like above?

 

[pancho_hideboo]

Re: Z11=input impedance?

ZPort Impedance.Whe you look through a port, the impedance which you'll see from this port.
ZM:Open circuited Z parameter.It's totally different than ZP because Z12 is not zero.
The impedance which you will measure with VNA will be ZP, NOT ZM.

Wrong, if you mean Post Processing of Cadence Spectre.

ZP ; Open circuited Z parameter
ZM ; Input impedance seeing from Port.

So the impedance which you will measure with VNA will be ZM, NOT ZP.

See https://www.edaboard.com/threads/166900/

 

[sharethewell]

Re: Z11=input impedance?

Wrong, if you mean Post Processing of Cadence Spectre.

ZP ; Open circuited Z parameter
ZM ; Input impedance seeing from Port.

So the impedance which you will measure with VNA will be ZM, NOT ZP.

I don't use a VNA. I just set up the schematic of the circuit in Cadence and run SP analysis. Don't know if you are talking about Vector Network Analyzer?

So ZM should be more accurate than ZP according to how my circuit is set up above?

For my output stage, using ZM1, I got negative real part. If I use ZP, I got positive real part. Don't know why? Any idea?

 

[sharethewell]

Re: Z11=input impedance?

Yes.

What do you mean by "output stage" ?
Do you mean output impedance ?
If so, simply your output impedance is dependent on load termination which is Rs in your schematic.

So you have to study source stabilty and load stability.

I mean the input impedance of the output stage. One is positive, the other is negative.

 

[sharethewell]

Re: Z11=input impedance?

Yes.

Simply your input impedance is dependent on load termination which is RL in your schematic.

ZM(1)@"RL=inf" = ZP(1,1)

Your circuit could be unstable for RL=50ohm.
So you have to check load stabilty

Also you have to check source stability.

ZM(1)@"Rs=inf" = ZP(1,1)？ So ZM1 is defined when impedance of the source is infinite?

How to check load stability and source stability respectively in Cadence? K factor?

 

[pancho_hideboo]

Re: Z11=input impedance?

I just set up the schematic of the circuit in Cadence and run SP analysis.
So ZM should be more accurate than ZP according to how my circuit is set up above?

Yes.

For my output stage, using ZM1, I got negative real part.
If I use ZP, I got positive real part. Don't know why? Any idea?

Simply your input impedance is dependent on load termination which is RL in your schematic.

ZM(1)@"RL=inf" = ZP(1,1)

Your circuit could be unstable for RL=50ohm.
So you have to check load stabilty

Also you have to check source stability.

See the followings.
The Designer's Guide Community Forum - SP simulation and negative real Y
The Designer's Guide Community Forum - Common Source LNA stability

ZM(1)@"Rs=inf" = ZP(1,1)？ So ZM1 is defined when impedance of the source is infinite?

No.

Read very basic text book on circuit theory.
Relation between ZM(1) and ZP(*,*) is like following.
Zin=ZM(1)=ZP(1,1) - ZP(1,2)*ZP(2,1)/{ZP(2,2)+RL}

So, if RL=infinite, ZM(1) is coincident to ZP(1,1).
In this case, analysis is one-port SP-analysis not two-port SP-analysis.

How to check load stability and source stability respectively in Cadence? K factor?

If you prefer Cadence Spectre, see figure in The Designer's Guide Community Forum - how to simulate noise matching for LNA in spectre?.
Here "LSB" is for "Load Stability" and "SSB" is for "Source Stability".

Your amplifiers are Class-F and Class-E, so you have to consider stability analysis under large signal drive not small signal analysis such as conventional SP-analysis which you do.

Also see the followings.
The Designer's Guide Community Forum - Very curious about optimum impedance from load-pull in PA designs

The Designer's Guide Community Forum - How to plot "input reflection coefficient" in ADS

The Designer's Guide Community Forum - Oscillation in PA

The Designer's Guide Community Forum - how to simulation the large signal stability of power amplifier?

 

[prcken]

Re: Z11=input impedance?

now by using ZP it is positive now? but i remember you have told me that it was still negative.
i dont know the difference between them, i never used ZM before, should read the manual

 

[BigBoss]

Re: Z11=input impedance?

Wrong, if you mean Post Processing of Cadence Spectre.

ZP ; Open circuited Z parameter
ZM ; Input impedance seeing from Port.

So the impedance which you will measure with VNA will be ZM, NOT ZP.

See https://www.edaboard.com/threads/166900/

You're right..
I have confused.Thanks for your correction.