# Calculating for impedance matching of more complex circuits

When I start off to calculate the impedance from Z-input, how can I reach to antenna's Z-output which may be variable, for example 50 ohm. I have several good links on Internet:

https://www.omnicalculator.com/other/impedance-matching

for impedance matching for several impedance types

https://keisan.casio.com/exec/system/1258032615

for impedance calculating of circuit components

https://www.omnicalculator.com/physics/capacitive-reactance

for calculating the reactance of capacitors

https://www.omnicalculator.com/physics/voltage-divider

voltage divider tool

Are there any tools on Internet, which calculate all impedances in circuit automatically, maybe freeware?

The circuit below is just an example for impedances, which I want to calculate. Especially, I want to know the Z-input and the Z-output. What if I want to boost the power to antenna by impedance matching for better and strong transmission.

+5V and GND are connections for power supply. I use DC voltage as the source and the input(+) is used for AC waves like sound from mp3 player, for example.

• Warez? I'm not familiar with anything by that name. The problem is that transistor there. What are you actually trying to do here? Jul 6, 2023 at 4:38
• This schematic took this electrical engineer twice as long as necessary to parse, because you put GND on top, and the positive supply voltage on bottom. Don't draw it that way, it confuses people :) Conventions are there for good reason. Also, why have the GND symbol and a net symbol "gnd"? That seems very unnecessary. Jul 6, 2023 at 10:14
• ok, I will try to correct the circuit above. Jul 6, 2023 at 15:08
• yeah, now it should be fine. I updated the picture. +5V and GND are connections for power supply. I use DC voltage as the source and the input(+) is used for AC waves like sound from mp3 player, for example. I hope, it helps. Thanks for watching. Jul 6, 2023 at 15:17
• @timwilliams I looked around for the mistake, yeah, it is not "free warez", but "freeware". So, I apology for that. I have corrected it instantly. The question about what the circuit above does is, the circuit is just a simple transmitter radio. Jul 6, 2023 at 15:34

As stated in the comments section of the original post, a correctly drawn schematic is much easier to comprehend. Jonk's posting for drawing schematics is a good read.

Since this is an oscillator with a crystal resonator, measuring the complex impedance at the base is a difficult task.

Personally, I wouldn't be concerned with impedance matching this sort of circuit since it's for short range communication. Connect a small length of wire (2 to 3 m) and see if it still oscillates. If it stops oscillating, shorten the wire. You should be able to get a couple metres range.

The impedance at the base is roughly 900 ohms in the simulation below. This was done measuring the output voltage, V(out), with R6 = 100g and at R6 = 10k with no modulation. With R6 = 100g, this gives the equivalent Thevenin voltage. With R6 = 10k you can figure out the equivalent Thevenin resistance using a bit of Ohm's law. This does not give you a proper complex impedance that you would need for matching but helps you understand the magnitude of the impedance at the base.

If you want to match this to a proper length antenna, use an emitter follower which will give you a lower output impedance. Since this is non-critical, forego a matching network. If you want to match with a matching network, use the first link in your post, or, you can have fun with a Smith Chart which its usage can be found on many web sites. Also consider an amplifier after the emitter follower if more range is desired.

As for the modulation input impedance, in SPICE you calculate the input Z with V(in)/I(R3). It will be higher than 33k.

C5 & R6 form a high-pass filter to eliminate the DC offset and the 1 kHz baseband modulation signal while minimally loading the base. A crystal is modeled with L1, R4, C2, C3. The values were taken from a random web site and adjusted to about 22 MHz.

• Thanks for this approaching. Could you tell me, if it is possible, when I would have soldered the antenna to bc547 transistor's collector in my drawing of circuit and would have an "out" resistor on it, so then I want to know what the Z output impedance shall be. Should I do V(in)/I(out) calculation? After all, whatever would come at the end, that will be impedance matched. Is that correct? Jul 7, 2023 at 0:09
• Another question goes to impedance calculation of components, which work with frequencies in AC. Which frequency should I consider? The frequency of AC input or the frequency of oscillator? Jul 7, 2023 at 0:19
• @lastime For the first comment, using the same technique to find the impedance at the base can be used to measure the impedance at the collector. That technique shows the impedance at the collector is around 50 ohms. Again, this doesn't give you complex Z, but gives a feel for the magnitude of the Z at the collector. As for your second comment, you are interested in passing the 20 MHz signal.
– qrk
Jul 7, 2023 at 21:32

You can use LTSpice for that, although you will have to find or fill in information for your crystal. See https://www.youtube.com/watch?v=S5ut1ef9c4s for the process of how to go about it. Note that LTSpice can also be used with custom formulas to find out more than impedance. Here is a screenshot for a previous project of mine.

• Thanks for useful answer. Can you give me just a hint, where to start off to make an impedance matching for given circuit, I am asking for in question above. Yes, I know LTSpice makes things uncomplicated, because I am using it, too. But the technical kick is just main issue, I need to make the circuit somehow matched. Jul 6, 2023 at 17:26
• @lastime If you are trying to impedance match stages in a design, you first need to calculate the impedances of the blocks that you are working with. That is where LTSpice can be handy. As for designing a matching circuit, you can find schematics online and test them with LTspice. Jul 6, 2023 at 17:30

This radio transmitter circuit above in the question is working for very short distances, so there is nothing special in this circuit to try on making the impedances matched. But there could be a high-pass filter in use at the input, while using an emitter-follower with amplifier at antenna should make the handwork for a stronger and better transmission.

Here is an example from:

https://semesters.in/emitter-follower-common-collector-transistor-amplifier-electronics-engineering-notes-1st-year/