Isolation and Impedance Matching

Transformers can provide isolation between electronic circuits. While there is inductive coupling in a transformer, there is comparatively little capacitive coupling. The amount of capacitive coupling can be reduced by using cores that minimize the number of wire turns needed in the windings, and by keeping the windings physically separated from each other (rather than overlapping).

Balanced and Unbalanced Loads and Lines

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At A, a balanced-to-unbalanced transformer. At B, an unbalanced-to-balanced transformer.
A balanced load is one whose terminals can be reversed without significantly affecting circuit behavior. A plain resistor is a good example. The two-wire antenna input in a television receiver is another example of a balanced load. A balanced transmission line is usually a two-wire line, such as oldfashioned TV ribbon, also called twinlead.

An unbalanced load is a load that must be connected a certain way. Switching its leads will result in improper circuit operation. In this sense, an unbalanced load is a little like a polarized component such as a battery or capacitor. Many wireless antennas are of this type. Usually, unbalanced sources and loads have one side connected to ground. The coaxial input of a television receiver is unbalanced; the shield (braid) of the cable is grounded. An unbalanced transmission line is usually a coaxial line, such as you find in a cable television system.

Normally, you cannot connect an unbalanced line to a balanced load, or a balanced line to an unbalanced load, and expect good performance. But a transformer can allow for mating between these two types of systems. In above Figure A, a balanced-to-unbalanced transformer is shown. Note that the balanced side is center-tapped, and the tap is grounded. In above figure B, an unbalanced to balanced transformer is illustrated. Again, the balanced side has a grounded center tap.

The turns ratio of a balanced-to-unbalanced transformer (also called a balun) or an unbalanced to balanced transformer (also known as an unbal) can be 1:1, but this need not be the case, and often it is not. If the impedances of the balanced and unbalanced parts of the systems are the same, then a 1:1 turns ratio is ideal. But if the impedances differ, the turns ratio should be such that the impedances are matched. Shortly, we’ll see how the turns ratio of a transformer can be manipulated to transform one purely resistive impedance into another.

Transformer Coupling

Transformers are sometimes used between amplifier stages in electronic equipment where a large amplification factor is needed. There are other methods of coupling from one amplifier stage to another, but transformers offer some advantages, especially in RF receivers and transmitters. Part of the problem in getting a radio to work is that the amplifiers must operate in a stable manner. If there is too much feedback, a series of amplifiers will oscillate, and this will severely degrade the performance of the radio. Transformers that minimize the capacitance between the amplifier stages, while still transferring the desired signals, can help to prevent this oscillation.

Impedance Transfer Ratio

In RF and AF systems, transformers are employed to match impedances. Thus, you will sometimes hear or read about an impedance step-up transformer or an impedance step-down transformer. The impedance transfer ratio of a transformer varies according to the square of the turns ratio, and also according to the square of the voltage-transfer ratio. If the primary (source) and secondary (load) impedances are purely resistive and are denoted Zpri and Zsec, then the following relations hold:
Zpri/Zsec = (Tpri/Tsec)2
Zpri/Zsec = (Epri/Esec)2

The inverses of these formulas, in which the turns ratio or voltage-transfer ratio are expressed in
terms of the impedance-transfer ratio, are:
Tpri/Tsec = (Zpri/Zsec)1/2
Epri/Esec = (Zpri/Zsec)1/2

Problem

Consider a situation in which a transformer is needed to match an input impedance of 50.0 ?,
purely resistive, to an output impedance of 300 ?, also purely resistive. What is the required turns ratio Tpri/Tsec?
The required transformer will have a step-up impedance ratio of Zpri/Zsec = 50.0/300 = 1/6.00.
From the preceding formulas:
Tpri/Tsec = (Zpri/Zsec)1/2
= (1/6.00)1/2
= 0.166671/2
= 0.408
= 1/2.45

Problem 2

Suppose a transformer has a primary-to-secondary turns ratio of 4.00:1. The load, connected to the transformer output, is a pure resistance of 37.5 ?. What is the impedance at the primary?
The impedance-transfer ratio is equal to the square of the turns ratio. Therefore:
Zpri/Zsec = (Tpri/Tsec)2
= (4.00/1)2
= 4.002
= 16.0

We know that the secondary impedance, Zsec is 37.5 ?. Thus:
Zpri = 16.0 × Zsec
= 16.0 × 37.5
= 600 ?