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. Thismaximal 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.
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:
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.
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
- max. Energy
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.
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.
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 therefore 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.
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.
How can a transformer be used for impedance matching? ›
Transformers. Transformers are sometimes used to match the impedances of circuits. A transformer converts alternating current at one voltage to the same waveform at another voltage. The power input to the transformer and output from the transformer is the same (except for conversion losses).What is impedance matching? ›
Impedance matching is designing source and load impedances to minimize signal reflection or maximize power transfer. In DC circuits, the source and load should be equal. In AC circuits, the source should either equal the load or the complex conjugate of the load, depending on the goal.Which type of transformer is used for impedance matching? ›
Audio transformers are used to match the load impedance to a source, which allows the maximum amount of power to be transferred to the load which can be explained by Jacobi's law.How do you determine impedance matching? ›
Impedance matching is the balance between the source and load impedance to ensure the load receives maximized power. Maximum power theorem is important in transferring energy from the source to the load. Impedance matching is needed to allow maximum power transfer from the source to the load by reducing reflections.What are the types of impedance matching? ›
Impedance matching devices can be separated into two categories: those that are lossy, implemented with resistive components; and those that are ideally lossless, using reactive components—inductors, capacitors, and transmission lines.What is the importance of impedance in transformer? ›
Why is impedance important? Impedance is the current limiting characteristic of a transformer and is expressed in percentage. It is used for determining the interrupting capacity of a circuit breaker or fuse employed to protect the primary winding of a transformer.What are the advantages of impedance matching? ›
Matching the impedances throughout the circuit yields a desired low voltage standing wave ratio (VSWR). Low VSWR circuits transfer the maximum amount of power from the source to the load. There's more. Digital circuits deliver desired performance because of short transition times and high clock rates.What is meant of impedance? ›
Impedance, denoted Z, is an expression of the opposition that an electronic component, circuit, or system offers to alternating and/or direct electric current. Impedance is a vector (two-dimensional)quantity consisting of two independent scalar (one-dimensional) phenomena: resistance and reactance.What is impedance matching and why is it important for hearing? ›
The major function of the middle ear is to match relatively low-impedance airborne sounds to the higher-impedance fluid of the inner ear. The term “impedance” in this context describes a medium's resistance to movement.How do you measure impedance? ›
Impedance is calculated by dividing the voltage in such a circuit by its current. In short, impedance can be described as limiting the flow of current in an AC circuit. Impedance is indicated by the symbol “Z” and measured in ohms (Ω), the same unit used to measure DC resistance.
What is the need to design an impedance matching network? ›
Impedance matching is necessary in RF circuit design to provide maximum possible power transfer between the source or the generator and the load.What are the three components of impedance? ›
What follows below is a derivation of impedance for each of the three basic circuit elements: the resistor, the capacitor, and the inductor. Although the idea can be extended to define the relationship between the voltage and current of any arbitrary signal, these derivations assume sinusoidal signals.Which two networks are used in impedance matching? ›
Generally the two networks, pi and T are used for impedance matching.What is the principle of impedance? ›
The principle of impedance counting, also known as the Coulter principle after its inventor Wallace Coulter, is the passage of cells suspended in a known dilution through a small orifice. The electrolyte-containing diluent serves as a conductor of a constant electrical current between two electrodes.What is the advantage of using matching? ›
Advantages of matching
Matching is a useful method to optimize resources in a case control study. Matching on a factor linked to other factors may automatically control for the confounding role of those factors (e.g. matching on neighborhood may control for socio-economic factors).
Which configuration is suitable for impedance matching? Explanation: CC has high input impedance and low output impedance. Hence suitable for impedance matching.What is the advantages of matching item? ›
Advantages of Matching Questions:
Less chance for guessing than other question types. Can cover a large amount of content. Easy to read. Easy to understand.
The unit of impedance, like that of resistance, is the ohm.What is an example of impedance? ›
Impedance Sentence Examples
Standard structured UTP or FTP cabling systems have a nominal impedance of 100 ohms. Having a high input impedance means it only takes very little capacitive coupling to get a reading.
the resistance is caused by the collisions of the electrons with the atoms inside the resistors. the impedance in a capacitor is caused by the creation of an electric field. the impedance in an inductor is caused by the creation of a magnetic field.
How do impedance matching networks work? ›
A matching network is connected between a source and a load, and its circuitry is usually designed such that it transfers almost all power to the load while presenting an input impedance that is equal to the complex conjugate of the source's output impedance.What happens if there is no impedance matching? ›
If the impedances aren't matched, maximum power will not be delivered. In addition, standing waves will develop along the line. This means the load doesn't absorb all of the power sent down the line.Why impedance matching is required What are other constraints required? ›
Modern digital and analog systems require impedance control and impedance matching due to the preponderance of components with fast rise time (less than a few ns) and low supply voltage, as well as analog components that are running at ever higher frequencies.Can a transformer change impedance? ›
The presence of a transformer can alter the impedance seen by a voltage source. This is not too surprising when we consider that impedance is related to voltage and current and that a transformer with N ≠ 1 alters the voltage across and current through a load component on the secondary side.Which transformer is used for impedance matching in transistor coupled? ›
Which transformer is used for impedance matching in transistor coupled amplifier? Explanation: Usually the impedance of an output device is a few ohms whereas output impedance of the transistor is several 100 ohms. In order to match the impedance a step down transformer of proper turn's ratio is used.What is impedance test of a transformer? ›
In this test, one set of windings is shorted (typically the LV windings) and a three-phase voltage source is applied to the other set of windings. The voltage is steadily increased until the rated phase current is measured. The voltage at this point is called the impedance voltage.Can we apply Ohm's Law in transformer? ›
A transformer as whole consists of two electrically isolated circuits. And as a whole transformer doesn't follow Ohm's law because when a voltage is increased, current decreases. Ohm's law is applicable in electrical circuits i-e primary winding and secondary winding individually.What is the effect of impedance? ›
In addition to resistance as seen in DC circuits, impedance in AC circuits includes the effects of the induction of voltages in conductors by the magnetic fields (inductance), and the electrostatic storage of charge induced by voltages between conductors (capacitance).What are the units of impedance? ›
The unit of impedance, like that of resistance, is the ohm.What is impedance and its types? ›
Impedance, denoted Z, is an expression of the opposition that an electronic component, circuit, or system offers to alternating and/or direct electric current. Impedance is a vector (two-dimensional)quantity consisting of two independent scalar (one-dimensional) phenomena: resistance and reactance.
Which law is used in transformer? ›
Transformers contain a pair of windings, and they function by applying Faraday's law of induction. AC passes through the primary winding, which creates a varying magnetic flux. The magnetic field that results strikes the second winding and generates an AC voltage in that winding via electromagnetic induction.Which rule is used in transformer? ›
According to Faraday's law, since the same magnetic flux passes through both the primary and secondary windings in an ideal transformer, a voltage is induced in each winding proportional to its number of windings. The transformer winding voltage ratio is equal to the winding turns ratio.What are the 3 main applications of Ohm's law? ›
Ohm's Law Applications
The main applications of Ohm's law are: To determine the voltage, resistance or current of an electric circuit. Ohm's law maintains the desired voltage drop across the electronic components. Ohm's law is also used in DC ammeter and other DC shunts to divert the current.