# RF Circuits Impedance Matching Basics

Impedance matching is a very basic and also important task for every RF engineer. The theory behind it is simple but sometimes it can be a very frustrating job for a RF person to get the matching done properly.

In this article, we will discuss the very basic impedance matching in a plain simple way to get you understand it without confusion, and help you work on your lab bench with confidence.

To keep things simple, we will not get transmission line involved and we assume all RF paths are very short, comparing with the wavelength at the operation frequency.

Fig. 1 Input and output impedance in a 2-port circuit

Most RF circuits such as amplifiers, transformers, isolators, couplers, dipexers, duplexers, attenuators, filters, etc. have 2 ports, input port and output port, and each port has its own impedance.

Both input and output ports need to be connected to certain external networks and, therefore, impedance matching to have the best power transfer is indispensable to RF design.

###### Understanding those basic parameters

- \(Z\) (impedance, complex number, in ohms), here are 2 examples of Z:
- \(Z_{in}=R_{in}+jX_{in}\), input impedance.
- \(Z_{out}=R_{out}+jX_{out}\), output impedance.
- \(Z_{s}=R_{s}+jX_{s}\), source impedance.
- \(Z_{L}=R_{L}+jX_{L}\), load impedance.

In order to get the optimal power transfer from a source to a load, the source impedance must equal the complex conjugate of the load impedance:

\(R_s+jX_s=R_L-jX_L\), so \(R_s =R_L\) and \(X_s=-X_L\)

Fig. 2 Optimal power matching between source and load

- \(Z_0=R_0\), characteristic impedance, is often a real industry normalized value, such as 50Ω (for RF/microwave) and 75Ω (for cable), etc. Unless otherwise stated, \(Z_0=50Ω\) in all circuits mentioned below.

###### Get maximal power output with impedance matching

The impedance of both input and output ports needs to be matched in order to get the maximal power at the output port.

Once the impedance matching is done, both impedance seen from the source and load is 50Ω.

Fig. 3 Input and output impedance matching

###### Impedance matching using lumped elements

We’ll only focus on the impedance matching using lumped elements since this is the most popular method applied in RF circuit design.

And we’ll only use lossless passive elements, inductors and capacitors, as the matching components.

There are many different combination of passive components to match a non-50Ω impedance, the answer depends on how conveniently you can get the job done.

Let’s start working on \(Z_{in}\) in Fig. 1.

Fig. 1 Input and output impedance in a 2-port circuit

For the reason of simplicity and convenience, we normalize \(Z_{in}\) to \(z_{in}\) which \(z_{in}=Z_{in}/50\).

Fig. 2 Normalized input impedance

Under a few certain situations, it would be better to transfer the impedance to admittance before applying matching process.

Fig. 3 Transfer impedance to admittance

Based on the values of r, g, x, and b, we can roughly categorize the impedance into 4 different types:

**Type #1**: r ≥ 1, x any value.**Type #2**: g ≥ 1, b any value.**Type #3**: r < 1, g < 1, x > 0 or b < 0.**Type #4**: r < 1, g < 1, x < 0 or b > 0.

Theoretically all these 4 types of impedance can be perfectly matched to 50Ω by using only 2 lumped elements, inductors and capacitors, if not considering the limited component values we are able to get as well as their tolerances.

###### Locate all types of impedance in the Smith chart

Each type of impedance can be conveniently and uniquely located in the Smith chart as showed below.

In the next article we’ll discuss how to match these 4 types of impedance by using lumped elements, inductors and capacitors, and calculate the element values using all formulas learned before.

You’ll also learn how to easily obtain the matching circuits without knowing those formulas, using Smith chart in a proprietary excel spreadsheet. The only data you need to enter are S11 or impedance need to be matched at a certain operation frequency.

You’ll be directed to download this unique spreadsheet for FREE after you have read through every article in this Smith chart sequence.

Fig. 4 A Smith chart template

**Type#1: r>1, x any value.**

Fig. 5 Type #1 impedance location in Smith chart

**Type #2: g>1, b any value.**

Fig. 6 Type #2 impedance location in Smith chart

**Type #3: r<1, g<1, x>0 or b<0.**

Fig. 7 Type #3 impedance location in Smith chart

**Type #4: r<1, g<1, x<0 or b>0.**

Fig. 8 Type #4 impedance location in Smith chart

Fig. 9 Four types of impedance in the Smith chart

Move on to the next article to learn how to easily match these 4 types of impedance using the Smith chart and a proprietary spreadsheet.

‘Note: This is an article written by an RF engineer who has worked in this field for over 40 years. Visit ABOUT to see what you can learn from this blog.’