# Introduction to impedance matching and how to use an impedance matching transformer in your design (2023)

If you are an RF design engineer or someone who has worked with wireless radios, the term “impedance matching' you should have noticed more than once. The term is crucial because it directly influences the transmission power and thus the range of our radio modules. This article aims to help you understand what impedance matching is from scratch and also to help you design your own impedance matching circuits using an impedance matching transformer, which is the most common method. So let's dive in.

### What is Impedance Matching?

In short, impedance matching ensures that theThe output impedance of a stage, called the source, is equal to the input impedance of the following stage, called the load. This adjustment enables maximum power transmission and minimum losses. You can easily understand this concept by thinking of it as lightbulbs in series with a power source. The first bulb is the output impedance for the first stage (e.g. a radio transmitter) and the second bulb is the load or in other words the input impedance of the second bulb (e.g. an antenna). We want to ensure that most of the power is delivered to the load, in our case this would mean that most of the power is transmitted into the air to allow a radio station to be heard from a greater distance. Themaximal Power transfer occurs when the output impedance of the source is equal to the input impedance of the loadbecause when the output impedance is greater than the load, more power is dissipated in the source (the first bulb glows brighter).

### Standing Wave Ratio – measure of impedance matching

A measurement used to define how well two stages are matched is calledSWR (standing wave ratio).It is the ratio of the larger impedance to the smaller, a 50Ω transmitter on a 200Ω antenna gives 4 SWR, a 75Ω antenna directly feeding an NE612 mixer (input impedance is 1500Ω) gives a SWR of 20. A perfect match, say a 50Ω antenna and 50Ω receiver gives an SWR of 1.

With radio transmittersSWR values ​​below 1.5 are considered decent, and operating at an SWR value above 3 can cause damage from overheatingthe power output devices (vacuum tubes or transistors). In receive applications, a high SWR does not cause any damage, but it makes the receiver less sensitive as the received signal is attenuated due to mismatch and resulting power loss.

Since most receivers use some kind of inputBandpassfilterthe front-end filter can be designed to match the antenna to the front-end of the receiver. All radio transmitters have output filters with which the power output stage is adapted to the specific impedance (usually 50 Ω). Some transmitters have built in antenna tuners that can be used to match the transmitter to the antenna if the impedance of the antenna differs from the output impedance of the specified transmitter. If there is no antenna tuner, an external matching circuit must be used. The performance loss due to mismatch is difficult to calculate, so special calculators orSWR loss tablesare used. A typical SWR loss table is shown below

Using the above SWR table, we can calculate the power loss and also the voltage loss. Voltage is lost due to mismatch when the load impedance is lower than the source impedance, and current is lost when the load impedance is higher than the source impedance.

(Video) Wideband coupling - Transformer Impedance matching (1/3)

Our 50Ω transmitter with a 200Ω, 4 SWR antenna loses about 36% of its power, which means 36% less power is delivered to the antenna than if the antenna had a 50Ω impedance. Most of the lost power is dissipated in the source, ie if our transmitter put out 100 W, an additional 36 W is dissipated as heat. If our 50Ω transmitter was 60% efficient, it would consume 66W sending 100W into a 50Ω antenna. When connected to the 200Ω antenna, an additional 36W is dissipated, so the total power dissipated as heat in the transmitter is 102W. Increasing the power emitted in the transmitter not only means that the full power is not radiated from the antenna, but there is also a risk of damaging our transmitter since it consumes 102W instead of the 66W for which it was designed.

In the case of a 75Ω antenna feeding the 1500Ω input of the NE612 IC, we are not concerned with the loss of power as heat but with the increased signal level that can be achieved using impedance matching. Let's assume that 13 nW of RF is induced in the antenna. With an impedance of 75Ω, 13nW gives 1mV - we want to match that to our 1500Ω load. To calculate the output voltage after the matching circuit, we need to know the impedance ratio, in our case 1500Ω/75Ω=20. The voltage ratio (like the turns ratio in transformers) is equal to the square root of the impedance ratio, so √20≈8.7. This means that the output voltage is 8.7 times larger, equivalent to 8.7 mV. The matching circuits act like transformers.

Since the power entering and leaving the matching circuit are equal (minus loss), the output current is lower than the input current by a factor of 8.7, but the output voltage is larger. If we matched a high impedance to a low one, we would get a lower voltage but a higher current.

### Impedance Matching Transformers

Special transformers called impedance matching transformers can be used to match the impedance. The main advantage ofTransformers as impedance matching devicesis that they are broadband, which means they can work with a wide range of frequencies.audio transformerswith steel cores, as used in vacuum tube amplifier circuits to match the high impedance of the tube to the low impedance of the speaker, have a bandwidth of 20 Hz to 20 kHz, RF transformers made of ferrite or even air cores can have bandwidths of 1MHz-30MHz.

Transformers can be used as impedance matching devices because their turns ratio changes the impedance that the source "sees". You can check this tooBasis des TransformatorsArticle if you are totally new with Transformers. If we have a transformer with a turns ratio of 1:4, this means that if 1V AC were applied to the primary winding, we would have 4VAC at the output. If we add a 4Ω resistor to the output, 1A of current will flow in the secondary, the current in the primary will be equal to the secondary current multiplied by the turns ratio (divided if the transformer was a step-down transformer, like mains transformers), so 1A *4=4A. If we use Ω law to determine the impedance that the transformer presents to the circuit, we have 1V/4A = 0.25Ω while we have a 4Ω load connected after the matching transformer. The impedance ratio is 0.25Ω to 4Ω or 1:16. It can also be expectedImpedance ratio formula:

`(NA/NB)²=rI`

where nAis the number of primary turns on the winding with more turns, nBis the number of turns on the winding with fewer turns and rIis the impedance ratio. This is how impedance matching happens.

(Video) EE310 Lecture 14A Impedance Matching with an Ideal Transformer

if we usedOhm's lawagain, but now to calculate the power going into the primary we would have 1V*4A=4W, in the secondary we would have 4V*1A=4W. This means our calculations are correct, that transformers and othersimpedance matching circuitsgive no more power than is given to them. No free energy here.

### How to choose an impedance matching transformer

A transformer matching circuit can be used if bandpass filtering is required, it should be resonant with the inductance of the secondary at the frequency of use. The main parameters of transformers as impedance matching devices are:

• Impedance ratio or more commonly expressed turns ratio(s)
• primary inductance
• secondary inductance
• primary impedance
• secondary impedance
• natural resonant frequency
• minimum operating frequency
• Maximum operating frequency
• winding configuration
• Presence of air gap and max. direct current
• maximum power

The number of primary turns should be sufficient so that the primary winding of the transformer has a reactance (it is an inductor) four times the output impedance of the source at the lowest operating frequency.

The number of turns on the secondary is equal to the number of turns on the primary divided by the square root of the impedance ratio.

We also need to know what type and size of core to use, different cores work well at different frequencies, outside of which they have losses.

(Video) RF Design-6: Smith Chart and Impedance Matching Fundamentals

The core size depends on the power that flows through the core, because every core has losses, and larger cores are better at dissipating those losses and not as easy to have magnetic saturation and other undesirable things.

An air gap is required when a direct current flows through any winding of the transformer when the core used is sheet steel, as in a power transformer.

### Transformer Matching Circuits - Example

For example, we need a transformer to match a 50Ω source to a 1500Ω load in the 3MHz to 30MHz frequency range in a receiver. We need to know first what core we would need as this is a receiver that has very little current going through the transformer so the core size can be small. A good core in this application would be the FT50-75. According to the manufacturer, its frequency range as a broadband transmitter is 1 MHz to 50 MHz, good enough for this application.

Now we need to calculate the primary turns, we need the primary reactance 4 times higher than the output impedance of the source, so 200 Ω. At the minimum operating frequency of 3MHz, an inductor of 10.6uH has a reactance of 200Ω. Using an online calculator we calculate that we need 2 turns of wire on the core to get 16uH, a little over 10.6uH, but in this case it's better to be bigger than smaller. 50Ω to 1500Ω gives an impedance ratio of 30. Since the turns ratio is the square root of the impedance ratio we get about 5.5, so for each primary turn we need 5.5 secondary turns to make the 1500Ω on the secondary look like the 50Ω Source. Since we have 2 turns on the primary side, we need 2*5.5 turns on the secondary side, i.e. 11 turns. The diameter of the wire should follow the 3A/1mm2rule (a maximum of 3 A flow per square millimeter of wire cross-sectional area).

Transformer matching is commonly used in bandpass filters toAdapt resonance circuits to low impedances of antennas and mixers. The higher the impedance loading the circuit, the lower the bandwidth and the higher Q. Very often, if we were to connect a resonant circuit directly to a low impedance, the bandwidth would be too large to be useful. The tank circuit consists of the secondary side of L1 and the first 220pF capacitor and the primary side of L2 and the second 220pF capacitor.

(Video) Getting Started and Impedance Matching with AWR - AWR Tutorial #1

The image above shows a Transformer adjustment used in avacuum tubeAudio power amplifier to match the 3000Ω output impedance of the PL841 tube to a 4Ω speaker. 1000pF C67 prevents ringing at higher audio frequencies.

### Autotransformer matching for impedance balancing

The autotransformer matching circuit is a variant of theTransformer Matching Circuit, where the two windings are connected on top of each other. It is commonly used inIF filter inductors, along with transformer matching to the base, where it is used to match the transistor's lower impedance to a high impedance that puts less stress on the tuning circuit and allows for smaller bandwidth and hence greater selectivity. The process for designing is virtually the same, with the number of turns on the primary equal to the number of turns from the coil's tap to the "cold" or ground end, and the number of turns on the secondary equal to the number of turns between the tap and the "hot" end or the end connected to the load.

The above image shows an autotransformer matching circuit. C is optional, if used it should be resonant with the inductance of L at the frequency of use. In this way the circuit also provides filtering.

This image shows an autotransformer and transformer matching used in an IF transformer. The high impedance of the autotransformer is connected to C17, this capacitor forms a resonant circuit with the entire winding. Because this capacitor is connected to the high-impedance end of the autotransformer, the resistive loading of the tuned circuit is higher, hence the circle Q is larger and the IF bandwidth is reduced, improving selectivity and sensitivity. The transformer match couples the amplified signal to the diode.

(Video) RF Design-7: Broadband and Multi-Stage Impedance Matching Design

Autotransformer matching used in a transistor power amplifier that matches the transistor's 12 Ω output impedance to the 75 Ω antenna. C55 is connected in parallel with the high-impedance end of the autotransformer, forming a resonant circuit that filters out harmonics.

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