How to calculate the value of Zin and Zout???

[samy555]

Can you please, help me in the calculation of input and output impedance of the following circuit:

View attachment 66322

This stage operates as the oscillator in a FM transmitter, and I want to put a matching Pi network between it and the 50 Ω antenna, so I need to calculate its input and output impedances.
Thanks

 

[canadaelk]

Google search on input impedance (one of so many!): http://www.geofex.com/Article_Folders/impednc.htm
Output impedance is (I am not into RF) much more complex and will depend on more variables, including the type of antenna used. E

 

[unclejed613]

the input impedance doesn't matter, as this is an oscillator. this is a terrible FM modulator, as it will have a huge AM component as well. look at a varactor modulated oscillator, as that will have very little effect on the amplitude, and the deviation will be adjustable.

 

[bloki]

Input impedance is important only at low audio frequencies. It is equal 47k || (h21*470)...~30k
Output impedance depends on Q of LC tank and h22 parameter of transistor. Since BC547 is not intended for HF applications the parameters at HF are not present. Impedance could be about 2k.
Simplest matching method is to choose apropriate tap from cold side of L (about 1 turn) to connect 50ohm load.

 

[samy555]

Input impedance is important only at low audio frequencies. It is equal 47k || (h21*470)...~30k
Output impedance depends on Q of LC tank and h22 parameter of transistor. Since BC547 is not intended for HF applications the parameters at HF are not present. Impedance could be about 2k.
Simplest matching method is to choose apropriate tap from cold side of L (about 1 turn) to connect 50ohm load.

Thank you bloki,,, I need to know how to calculate the output impedance
Regardless of the type of the transistor
Suppose that this transistor is RF type
I need mathematical formulas to perform calculations.
Chinese do this, see this circuit from:
http://www.talkingelectronics.com/projects/27MHz Transmitters/27MHzLinks-1.html
**broken link removed**

 

[languer]

Google the hybrid-pi model.

https://en.wikipedia.org/wiki/Hybrid-pi_model
https://www.electro-tech-online.com/custompdfs/2012/08/04.pdf

 

[samy555]

Google the hybrid-pi model.

https://en.wikipedia.org/wiki/Hybrid-pi_model
https://www.electro-tech-online.com/custompdfs/2012/08/04.pdf

These links are not useful here, because the transistor operates in the high frequency
What was in those links talks about the low frequencies which is easy and a lot of books talk about in detail
But I thank you for trying to help

 

[ccurtis]

It's an interesting calculation, I'm sure, and I'm not up to it. Maybe someone else is. For an accurate calculation, you need the S-parameters for the transistor at the bias and frequency you are using; which acquiring is a task unto itself.

What I can say is that the output impedance is very roughly equal to the 5.6pf capacitor in series with the 470 ohm emitter resistor. The capacitance between the collector and emitter of the transistor is a few picofarads added to the 5.6pf capacitor, so make it a total of 9pf, give or take. That's about 500 ohms at 100 MHz (470-j185). I want to point out that the purpose of matching impedances is to give maximum power transfer from output to input. Generally you don't want to take any power (or only a minimal amount) directly from the oscillator as a varying load will pull it off frequency and may affect its stability, if not stop the oscillator altogether. You will very likely kill the oscillator if you put a matching 500 ohm load on it. Ideally an active buffering circuit (as built around a FET, for example) with a stable, high input impedance and a 50 ohms output impedance should be used.

 

[languer]

These links are not useful here, because the transistor operates in the high frequency
What was in those links talks about the low frequencies which is easy and a lot of books talk about in detail
But I thank you for trying to help

Wow, spoken like someone who has designed tons of high frequency electronics. So let me see if I get this right; you've obviously designed several high frequency circuits so you are able to discern how to properly model the transistor at high frequencies. Which by the way; what do you call high frequencies (if we go strictly by the definition; that would be from 3MHz to 30MHz - which the model would be sort of close; if you talk about very high frequencies that would be 30MHz to 300MHz - which the model would still be close after adding some parasitics, lead inductances, and stray capacitances). But I am turning away from the subject, I apologize. So how does a High Frequency designer such as yourself go and look for the impedances of a bipolar transistor. Well of course you would not use the Hybrid model, because nobody would use such a simple model (https://www.electro-tech-online.com/custompdfs/2012/08/bjt_models.pdf, https://www.electro-tech-online.com/custompdfs/2012/08/bjt_model.pdf, https://www.ajol.info/index.php/bajopas/article/viewFile/58535/46880). In fact; no one in the RF industry attempts at simplifying the models so they contain just the necessary parameters to satisfy the modeling requirements for the given application/frequency. No we actually take the most complicated model we can find and we crank the computer optimizing power until there is no more juice left. And then we add some EM modeling capability so we make sure that our 27MHz design (which you may be making on a Perfboard with no concern whatsoever for strays, coupling, grounding, microstrip or stripline impedances) is just right on. Right; I bet this is how you approach this design.

But no real designers would not use such simple tools. So you want to know how to calculate the input and output impedance; the way the big boys do it right. Well here it is: calculate or measure the S-parameters on a calibrated set on a network analyzer. Calculate the input reflection paramter (gamma-in) and the output reflection coefficient (gamma-out). If you are lucky, your amplifier will have infinite reverse isolation and Gamma-In will equal S11, and Gamma-out will equal S22. But because I see you are not keen on simplifications and using lower-form models; assume you have to do the full calculation. Now it is a simple matter to make sure you present the input of the transistor/amplifier with a conjugate match at the input, and a conjugate match at the output. But wait, just to make it complete you have to take into consideration that the transistor may oscillate at maximum available gain. So you better draw all this on a Smith Chart and plot the input and output stability circles. On top of this draw the gain circles and chose the circle which provides adequate gain, yet ensures the transistor is stable. Now you can relax and calculate your conjugate matches to make sure you're all good.

Sounds like what you're looking for right. BTW, I guarantee you this. You'd be lucky if these "chinese" friends of yours which you are quoting for the 27MHz RC are doing something even remotely close to the very basic hybrid-pi model. But hey, you're the big shot right - so go have a blast.

 

[samy555]

Is the following true?
1- The 2nd transistor acts as an oscillator, so the 1n cap made it a common base?
2- Since the 1st stage is a voice preamplifier so it supply a low frequency signal to the 2nd, that is the 1st see the 2nd as a common emitter?

thanks

 

[ccurtis]

Is the following true?
1- The 2nd transistor acts as an oscillator, so the 1n cap made it a common base?
2- Since the 1st stage is a voice preamplifier so it supply a low frequency signal to the 2nd, that is the 1st see the 2nd as a common emitter?

thanks

Yes, the oscillator is Colpitts type with common base transistor amp. The output of the first stage changes the base bias of the osc transistor, thus slightly changing the equivalent capacitance of the transistor, thus changing the oscillator frequency (and the amplitude slightly, too).

BTW, I modeled the oscillator in LTSpice for fun. The output impedance of the model is 700-j200 at 100 MHz. You can use that as a starting point to match the oscillator to 50 ohms using a conjugate matching network and expect about 1.5 mW output power, and its stable (for wideband FM operation, anyway) . If the matching network you use has a DC path to ground at its input (such as through an inductance and/or resistance), use a 10n or larger capacitor between the output of the oscillator and the matching network to block DC.

 

[samy555]

Yes, the oscillator is Colpitts type with common base transistor amp. The output of the first stage changes the base bias of the osc transistor, thus slightly changing the equivalent capacitance of the transistor, thus changing the oscillator frequency (and the amplitude slightly, too).

BTW, I modeled the oscillator in LTSpice for fun. The output impedance of the model is 700-j200 at 100 MHz. You can use that as a starting point to match the oscillator to 50 ohms using a conjugate matching network and expect about 1.5 mW output power, and its stable (for wideband FM operation, anyway) . If the matching network you use has a DC path to ground at its input (such as through an inductance and/or resistance), use a 10n or larger capacitor between the output of the oscillator and the matching network to block DC.

That was the realistic and practical answer
I've already download LTspice IV program
And I am currently studying its "LTspiceGettingStartedGuide"
In the meantime, I hope you can send me the executable file and give me a brief idea of how you get "The output impedance of the model is 700-j200 at 100 MHz"
Thanks in advance

 

[ccurtis]

That was the realistic and practical answer
I've already download LTspice IV program
And I am currently studying its "LTspiceGettingStartedGuide"
In the meantime, I hope you can send me the executable file and give me a brief idea of how you get "The output impedance of the model is 700-j200 at 100 MHz"
Thanks in advance

Attached is a screen-shot and LTSpice .asc file. As for determining the output impedance of the model, I used a bit of trial and error with the simulation. We know that the output impedance is roughly 470 ohms (emitter resistor) and capacitive (roughly 9 pf). So, I put a 470 ohm load resistor in series with enough inductance to counteract the capacitive reactance and connected the series combination to the output of the oscillator through a 100n DC blocking capacitor. Next I did a parameter sweep simulation of the inductance and selected the inductance that gave the greatest output current through the load resistor. Next I did a parameter sweep of the load resistor to find the load resistor that provided the greatest peak output power (700 ohms). The output impedance is determined by calculation from those two values and the frequency of operation (700-j200).

In the attached model, I matched that output impedance to 50 ohms using an L matching circuit, calculated via on online calculator.

 

[samy555]

Thank you very much
I need some time to understand and analyze this clarification and I will reply tomorrow
Of course, there will be more questions
I hope that you accept
Thank you a gain for that excellent help

 

[ccurtis]

You're welcome. I'm happy to help where I can. If I don't respond right away, it just means I'm away. I'll be checking back in, though.

 

[audioguru]

The output swing is only 0.33V peak which is 233mV RMS. Then the output power into 50 ohms is only 1.1mW which is almost nothing.

If the 50 ohm antenna is connected directly to the collector of the oscillator transistor then the oscillator probably will not oscillate.
Add an RF amplifier transistor to isolate the oscillator from the antenna. Then the frequency will not change when something moves toward or away from the antenna.

The preamp does not have pre-emphasis (treble boost) so the de-emphasis in all FM radios will muffle the sounds.

 

[samy555]

We know that the output impedance is roughly 470 ohms (emitter resistor) and capacitive (roughly 9 pf).

(1) I have seen many articles, no one of them says that the output impedance related to RE (the 470 ohm), But says that it relates with RC. Can you please explain that point?
(2) capacitive (roughly 9 pf)??? we have 5.6pF + 3.4pF transistor internal capacitance, Did you mean that the number 9 came from the fact that these two capacitances are in parallel?
(3)I think that the above resistance and capacitance are connected in series?

So, I put a 470 ohm load resistor in series with enough inductance to counteract the capacitive reactance and connected the series combination to the output of the oscillator through a 100n DC blocking capacitor. Next I did a parameter sweep simulation of the inductance and selected the inductance that gave the greatest output current through the load resistor.

Like this?
**broken link removed**

but when simulate it I found that the inductance that gave the greatest output current through the load resistor = 500nH, and the current = 2.25mA
**broken link removed**

Next I did a parameter sweep of the load resistor to find the load resistor that provided the greatest peak output power (700 ohms)

I do that:
**broken link removed**
and get
**broken link removed**
the green curve is when R = 100 ohm

The output impedance is determined by calculation from those two values and the frequency of operation (700-j200).

I dont understand how!

In the attached model, I matched that output impedance to 50 ohms using an L matching circuit, calculated via on online calculator.

I go to the https://www.changpuak.ch/electronics/calc_18.php# page but cannot do anything

I tried to do my best in order to understand
Experimented and read dozens of pages
But I did not go out the outcome of the task, so please help

 

[ccurtis]

Hi again. Let's take this one at a time.

1) I have seen many articles, no one of them says that the output impedance related to RE (the 470 ohm), But says that it relates with RC. Can you please explain that point?

The collector load does apply, but the collector load in the circuit at issue is a LC resonant tank with a very high impedance so it is insignificant. A perfect resonate tank has a theoretically infinite impedance. The emitter resistor must apply because the oscillator current flows through the emitter resistor too.

(2) capacitive (roughly 9 pf)??? we have 5.6pF + 3.4pF transistor internal capacitance, Did you mean that the number 9 came from the fact that these two capacitances are in parallel?

Yes

(3)I think that the above resistance and capacitance are connected in series?

Yes.

Like this?

but when simulate it I found that the inductance that gave the greatest output current through the load resistor = 500nH, and the current = 2.25mA

I do that:
and get
the green curve is when R = 100 ohm

Yes, that's what I did, only I get 550 ohms, not 100 ohms, so you might want to run that again.

That's still different than the 700-j200 I mentioned previously. I can only assume I had a different transistor in the model when I figured the output impedance of 700-j200 and then put the BC547 in there later. I was experimenting with different transistors at the time and I probably got my models confused. But, what you describe is how I came up with the output impedance for the model. Sorry for the confusion.

I go to the https://www.changpuak.ch/electronics/calc_18.php# page but cannot do anything

I tried to do my best in order to understand
Experimented and read dozens of pages
But I did not go out the outcome of the task, so please help

You did good. I used the following site to figure the matching network from the output impedance.

https://bwrc.eecs.berkeley.edu/research/rf/projects/60ghz/matching/impmatch.html


Edit: Wait a minute. I just realized you didn't look at peak power when you did a parameter sweep of the resistor value. You are looking at current. To plot power hold the Alt key down and left click on the resistor.