RC Networks and complex numbers

[OnceMore]

Hello.

I maybe should have put this in the maths section, but it is related to electronics, so I figured here.

I am reading Microwave Engineering by Pozar, and in one of the examples, it says that the series RC load impedance is Z_L = 60 - j80, so the resistance is 60 Ohms and the capacitance is 0.995pF. But is doesn't expalin how that C value was arrived at.

I was initially thinking that this was arrived at by comverting to polar form, but that doesn't seem to be it.

Could someone please help me with this?

Thanks.

-S

 

[sandy.bridge]

The impedance of a capacitor is given by,
$$Z_C=\frac{1}{j\omega{C}}$$
which given a RC network, would be associated with the imaginary component on the complex plane.

 

[OnceMore]

Thanks :)

Okay, so, I know the frequency is 2GHz, which gets me ω. But what is Z_c, is that the 80 in the complex number?

-S

 

[sandy.bridge]

Yes. The impedance of a network is given in the form Z=R+jX, where resistances are the real parts, and inductors and capacitors are the imaginary part. By plugging your values into the equation I gave you, you will indeed see that it is -j80!

 

[OnceMore]

I get it now.

Many thanks!

-S