## Tuesday, December 23, 2008

### Impedance matching in RF circuits

Impedance matching is one of the most important things of RF circuits.It is used for the purpose of transffering maximum power into a load circuit.Let's make it clear:

Suppose,you have a RF amplifier and it has an output impedance of 50 ohm.You also have an antenna that has an impedance of 75 ohm.Here the amplifier is the source and the antenna is the load.If you want to transfer the maximum possible power into the load (antenna) the source impedance must be matched to the load impedance.

Methods of Impedance Matching

There are several techniques used for impedance matching in RF circuits.They can be catagorised into two main types- transformer matching and LC type matching.At first we will discuss some LC type matching networks and show how to design them.
There are a number of LC type impedance matching networks such as the L network,T network,Pi network,split-capacitpr network and some other derivations.

Before going to discuss the networks we have to talk about notations.In all the circuits of this writing R1 is source resistance or impedance and R2 is the load resistance or  impedance .Inductors and capacitors  are noted with L and C.Inductive and capacitive reactances are noted with XL and Xc.

The L ntework

The L network is one of the simplest networks for impedence matching.It consists of a coil and a capacitor.
See figure 1 for network details and formulas for calculating every component value.The network of figure 1 calls for R1 to be greater than R2.This network can be used when R2 is greater than R1 but the capacitor should be used across the load.The L network is normally used for circuits of semi-widebandwidth.

The Inverse L Network

This is a variation of the L network.It is used when R2>R1.See figure 2 for this network.Everything is like the previous L network.You can calculate component valus from the formulas given in figure 2.

The Pi Network

The network of figure 3 is called the Pi matching network because it looks like the Greek letter 'Pi'.
It is widely used for impedance matching purposes.It can be used both in R1>R2 and R2>R1 requirments.But here we give the formula for when R1>R2.The pi network is bi-lateral so you can use any port for source or load.For calculating the component values first we have to define a Q value.You can get the minimum Q value needed from the formula given in figure 3.You can use a greater value but rember that high Q makes the bandwidth lower.After defining the Q use other formulas to calculate component values.

The Split-capacitor Network

This network is like the Pi matching network and chiefly used when  R2 > R1.Following figure 4 you can calculate the component values easily.

Rember: All the above networks and formulas are given considering R1 and R2 are pure resistive impedances and no reactive impedance is present.But they are applicable in many real world circuits where the reactive part is negligible.

Impedance matching is a vast thing to discuss.We wll complete our discussion gradually.If this