L-Network Question

[rcbuck]

I have been playing with L-Network matching circuits. Is there a formula that can be used to absorb the load series capacitor into the L-network?

For instance, in the attached schematic, assume the load is a crystal filter with an impedance of 210 ohms. The source impedance is 50 ohms as indicated. The design frequency is 9.0 MHz. I want to absorb the 88 pF cap into the L-network as that is one less component to deal with. The values shown for the L-network assume the load is 210 ohms including the 88 pF series capacitor.

Edit: Forgot to add schematic jpeg

[Neganur]

Is C2 Part of the crystal?
Do you happen to have the part number of the crystal?

[rcbuck]

No, C2 is not part of the crystal. It is the series resonating cap that changes the frequency of the first crystal in the filter. The part number of the crystal doesn't matter.

[yl3akb]

I have been playing with L-Network matching circuits. Is there a formula that can be used to absorb the load series capacitor into the L-network?

For instance, in the attached schematic, assume the load is a crystal filter with an impedance of 210 ohms. The source impedance is 50 ohms as indicated. The design frequency is 9.0 MHz. I want to absorb the 88 pF cap into the L-network as that is one less component to deal with. The values shown for the L-network assume the load is 210 ohms including the 88 pF series capacitor.

I like graphical approach better, when it comes to matching these circuits. Of course, You can absorb C2. L1,C1 and C2 transforms 50 ohms to Z = 209-j199 ohms. The same impedance can be obtained with L1=2.34uH and C1=160pF. See Smith chart graphs how it is obtained.

[rcbuck]

yl3akb, thanks for that reference. I knew it could be done with Smith chart. I was hoping there was a formula (or formulas) that would work.

I tried using SimSmith to perform the task. But I kept coming up with numbers that I knew were wrong. I guess I need to learn how to use Smith chart. I know W2AEW has few youtube tutorials on how to use it.

[KJDS]

The formulae are given in Rhea's Yin and Yang of Smith chart matching.