This page investigates the impendance in a 3 pole antenna matching filter.

If you follow the text below you will understand the match of an antenna to a transmitter.

I have used lot of jw-calculation, and if you don't know this method you can still follow the text and see the result in figures and diagram.

All contribution to this page are most welcome

The reason I am doing this page is because I didn't really understod the output filter from a class-C transmitter to the antenna. Most often there is a coil and two capacitor. To really understand this I went back to my old school-books and picked up the jw (J-Omega) method. This method substitut inductances and capacitances with reactances. The resistors is still the same.

The nice thing with jw is that when you have subsituted the capacitor and the inductor you can see them as resistors and then you can use the same method to calculate resistans as in a simple DC measurment. It sound complicated, but look at the figure below and I will explain.

Figure 1. shows an output filter connected to an antenna. This filter is supposed to be matched for an 50 ohm antenna at 50MHz.

This far you are still with me. If we look into figure 2 we can see that the antenna is substituted with a 50 ohm resistor to ground. The antenna acts as a resistor and in this case the antenna was 50 ohm so there is nothing strange here.

If figure 3 I have substituted all elements to impedances (Z). Remember I told you it was possible and I will tell you later how. Z4 is for example the 50 ohm resistor and Z2 is the coil. Don't mind about any values right now, we comes to that later.

Since all element is impedances I can calculate on this schematic as if it would be resistors. I can now use all the rules one use in DC calculation. For example

Don't forget it is the

I use a metod called jw. It is a mathematic way where you use complex values. Real and Imaginary numbers. I will not explain more about real and imaginay numbers, because you will have to learn it from basic in some math-book. If you know a little you can easy follow this.

What one does is to substitut the capacitor value to

The inductor is substituted with

the w (Omega) is equal to 2*pi*frequency w=2*pi*f

I now know how to substitut the L and C to impedances and I know how to calculate the

What I will do now is to put the XC = (1/jwC) and XL = (jwL) expression in formula and find the final formula for

In the first 2 expressions (red boxes) I calculate Z3 parallel with Z4 and the next red box is Z2+ Zant. See figure 4 at the top.

The rest is for calculating

If I put the components value in this formula for R, L and C and 2*pi*50MHz for the w-calculation I will get the impedance from this filter (Ztot).

I have made impedance calculation for different frequency and plotted them in a diagram (next picture). Please look at it and you will understand what this formula has calculated.

To see what the impedance curve would look like, I started to calculate the impendace at 30MHz and increased 1MHz untill 66MHz. The values are plotted in a diagram.

The blue line represent the

How did I get the components value from the begining?

I used a filterprogram for this and we can now be sure that the filterprogram calculated it right.

One main reason to use a filter is to filter away overtones from the carrier.

I have made a simulation of this filter and below you can se the frequency respons from this filter. The Y-axle show the attenuation in dB at the antenna side.

At 50Mhz there is no attenuation but you can see the higher frequency the more attenuation. Remember that the scale is logarithmic soo the attenuation is quit good.

I started with an output filter of descrete components. Then I transformed the antenna and the rest of the components to impedances. Then I transfomed the inductances and capacitances to reactances with jw-method and put it all in one big equation. (Puhhh...)

After some confusion I got the final formula (in the red rectangle) for impedance.

I know the values of the components and I calculated the impedance for different frequency and found out that the impedance at 50MHz actually is 50ohm.

This was a small introduction to jw calculation on filter and I hope you understod some of it.

Copyright © Last modified on 29th mars 2002.