The workings of RF transformers - Part 1

RF transformers are widely used in electronic circuits for impedance matching to achieve maximum power transfer and to suppress undesired signal reflection, voltage or current step-up or step-down, DC isolation between circuits while providing efficient AC transmission and interfacing between balanced and unbalanced circuits such as amplifiers.

When signal current goes through the primary winding, it generates a magnetic field that induces a voltage across the secondary winding. Connecting a load to the secondary causes an AC current to flow in the load.

It is generally necessary to control terminating impedances of RF signal paths, especially in wideband applications where path lengths are not negligible relative to wavelength. Wideband RF transformers are wound using twisted wires which behave as transmission lines and the required coupling occurs along the length of these lines as well as magnetically via the core.

Optimum performance is achieved when primary and secondary windings are connected to resistive terminating impedances for which the transformer is designed.

Transformers having a turns ratio of 1:1, for example, are typically designed for use in a 50 or 75 Ω system.

In this article, reference is continually made to terminating impedances which the user should provide for transformers, both for performance testing and in actual use.

For the sake of consistency, transformers with a turns ratio greater than 1:1 will be described as step-up; that is, the secondary impedance is greater than the primary impedance. In actual use, however, connection can be step-up or step-down as needed.

In Figure 1, three transformer winding topologies are illustrated. The one in Figure 1a is the simplest. Called an autotransformer, this design has a tapped continuous winding and no DC isolation. The transformer in Figure 1b has separate primary and secondary windings and provides DC isolation.

Figure 1a: Autotransformer.                                 Figure 1b: Transformer with DC isolation.

The RF performance of these configurations is similar, however.

That is, the impedance ratio is the square of the turns ratio.

The secondary winding in Figure 1c has a centre-tap, which makes the transformer useful as a balanced signal splitter. Excellent amplitude and phase balance are obtainable with well-designed RF transformers having this configuration.

Figure 1c: Transformer with centre-tapped secondary.

A variation on the transformer of Figure 1c, favouring high frequency performance, is shown in Figure 2. It adds a transmission-line transformer in cascade at the input, to convert an unbalanced signal to balanced at the input to the centre-tapped transformer. Features of this design are:

• Wide bandwidth, exceeding 1000 MHz;
• Good amplitude and phase balance;
• Higher return loss (lower VSWR) on the primary side.

Figure 2: High-frequency transformer with balun on primary side.

Insertion loss of a transformer is the fraction of input power lost when the transformer is inserted into an impedance-matched transmission system in place of an ideal (theoretically lossless) transformer having the same turns ratio.

Actual insertion loss is affected by non-ideal characteristic impedance of the transformer windings, as well as winding and core losses.

Typical insertion loss variation with frequency is illustrated in Figure 3, which shows the 1, 2, and 3 dB bandwidths, referenced to the midband loss as they are usually specified. Insertion loss at low frequency is affected by the parallel (magnetising) inductance.

Figure 3: Typical frequency response of an RF transformer.

At low temperature, low-frequency insertion loss tends to increase because of decreasing permeability of the magnetic core. High-frequency insertion loss is attributed to interwinding capacitance and series (leakage) inductance.

At high temperature it tends to become greater due to an increase in the loss component of core permeability.

A further influence on transformer insertion loss is high AC or DC current. Most RF transformers are used in small-signal applications, in which typically up to 100 mW of RF or 20 mA of unbalanced DC current pass through the windings.

In the interest of small size and widest bandwidth, the smallest practical size of cores is used. When insertion loss specifications must be met with greater RF power or DC current applied, this must be taken into account in the transformer design to prevent saturation of the core and consequent bandwidth reduction.

How is insertion loss of a transformer measured? This question is especially pertinent for impedance ratios other than 1:1 because accommodation must be made for the impedance of test instrumentation, which is generally a constant 50 or 75 Ω. There are three methods:

• Three transformers are tested in pairs: A and B, A and C, B and C. Each pair is measured back-to-back; that is, the high-impedance windings are directly connected to one another and the low-impedance windings face the source and detector of the instrumentation which match the transformer impedance. This results in three values of combined insertion loss, so that the values of the three unknowns (the individual A, B, C insertion losses) can be calculated.
• A transformer is measured individually with a minimum-loss pad as a matching circuit connected between the high-impedance winding and the instrumentation. This has been found practical for testing 50 to 75 Ω transformers, for which matching pads are readily available. The loss of the matching circuits (in dB) has to be subtracted from the measured value to yield the insertion loss of the transformer itself. This method is applicable where only two connections are made to the secondary. Figure 4 shows the performance of a 50 to 75 Ω transformer, model TC1.5-1, tested by this method. The loss of the matching pad was determined by measuring two of them back-to-back and dividing the dB-value by 2.
• If the transformer has a centre-tapped secondary winding, then it can be connected as a 180° power splitter. Each half of the secondary must be terminated by an impedance N² Z₁ ÷ 2. This requires a matching network to be used between the transformer and the sensing test-port of the insertion loss instrumentation. Because an individual test port sees only one output, both 3 dB for the split and the loss of the matching network must be subtracted from the measured value of insertion loss. By sensing both outputs, amplitude and phase unbalance can also be measured by this method. Element values and loss of the matching network are listed in Table 1.

Figure 4: Model TC1.5 - 1 insertion loss.

Table 1: Matching networks for testing centre-tapped transformers.

Note: Because instrumentation requiring proper source termination is connected to one or both outputs in this method, special design considerations apply to the matching network and it should not be a minimum-loss pad. This is discussed in detail later where design criteria, element values and insertion loss for suitable matching networks are given.

To demonstrate the usefulness of this method for centre-tapped transformers having a wide range of impedance ratios (N² values), insertion loss vs frequency is shown in Figures 5, 6, and 7.

Figure 5: Model ADTT1-1 insertion loss.

Figure 6: Model ADT4-1WT insertion loss.

Figure 7: Model ADT16-1T insertion loss.

 

To be continued