# Design high-performance pulse transformers in easy stage

Vincent J Spataro, GEC Marconi Electronic Systems Corp -March 16, 1995

Both analog and digital designers use pulse transformers to perform a multitude of functions. This article enables you to quickly and easily design pulse transformers for various applications. A step-by-step design procedure walks you through all the basic stages. PSpice modeling shows you how to verify your design.

In general, a pulse transformer transfers a pulse of current or voltage from the primary, or generating, side of the circuit, to the secondary, or load, side of the circuit. The pulse is usually rectangular, and maintaining the fidelity of its shape is important. As engineers work with increasingly higher frequencies, they must take greater care when designing pulse transformers. Typical applications of pulse transformers include voltage- and current-level transformation, dc isolation, matching impedances, polarity inversion, and providing gate-drive-to-FET or base-drive-to-bipolar transistors.

Taking the mystery out of pulse-transformer design means first understanding the fundamentals. Your requirements probably mandate a transformer with fast rise and fall times along with a minimum of overshoot and ringing. Luckily, you can realize high-performance designs with minimal effort by applying some simple design rules. Simple approximations quickly produce a workable design. You can then optimize your design in-circuit or by using a circuit-analysis tool, such as Spice. Finally, you can either fabricate a custom design or evaluate off-the-shelf pulse transformers.

Anatomy of a pulse

Ideally, a pulse's waveform should be perfectly rectangular, and all signal transitions should take place in zero time. In the real world, pulses can only approximate this ideal. Because current cannot change instantaneously, finite rise and fall times result. Parasitic elements cause overshoot and ringing. And nonideal components cause the flat portions of the pulse to deviate from a perfect plateau. Fig 1 shows a typical nonideal pulse at the output of a pulse transformer. (By convention, the rise time is the time the amplitude of the signal takes to go from 0.1 to 0.9 of its maximum value.)

Figure 1 Ideally, a pulse's waveform should be perfectly rectangular in shape. In the real world, pulses can only approximate this ideal.

Fundamentally, a typical pulse has four regions: the rising edge, the flat top of the pulse, the falling edge, and the trailing edge. Therefore, a separate circuit model can represent the pulse transformer in each of the four regions.

Region 1, the rising edge, occurs in response to the transition of the input signal from the low or ground state to a high-level state. Region 2, the flat top of pulse region, occurs later, when rising-edge transients are no longer present and the amplitude of the pulse is approximately a constant value. Region 3, the falling edge, is analogous to the rising edge, with the transition going from a high level to a low level. Region 4, the trailing end, occurs after the falling-edge transients have settled out and the signal is at a constant low level.

The rising and falling edges of the pulse are usually short compared to the flat top or trailing end of the pulse. This fact allows you to consider each region to be somewhat independent of the other regions, greatly simplifying analysis. The analysis can reconstruct the pulse's time period by superposition of the results for each region. The circuit models for each region are tractable using basic circuit-analysis tools and help you extract useful information about the transformer's behavior.

Basic circuit model

Before considering the electrical models for each region of the pulse, first examine a typical circuit employing a pulse transformer (Fig 2a). VI is the source of the rectangular pulse, or train of pulses, applied to LP, the primary inductance of the transformer. The characteristic impedance of VI is the resistance, RS. LS represents the secondary inductance of the transformer, which has a 1:n primary-to-secondary turns ratio.

Figure 2 In a typical pulse-transformer circuit (a), VI is the source of the rectangular pulse, or train of pulses, applied to LP, the primary inductance of the transformer. The characteristic impedance of VI is the resistance, RS. The more detailed model in (b) has an ideal transformer of turns ratio 1:1/a directly following a nonideal transformer of turns ratio 1:1.

One of three common termination schemes could be on the secondary side of the transformer. The first is R'ST, a series-terminating resistor. The second is R'PT, a parallel-terminating resistor. Capacitor C'pt, the third case, models a capacitive load. These three terminations cover most practical situations without oversimplifying the problem. Your circuit may contain one, two, or all three elements on the secondary side of the transformer.

The equations in this article account for all three terminations; eliminate the terminations that you do not require. If you have a situation that requires additional secondary elements, modify the equations to include them.

The more detailed model in Fig 2b (Ref 1) also represents the ideal transformer. In Fig 2b, an ideal transformer of turns ratio 1:1/a directly follows a nonideal transformer of turns ratio 1:1. V'O is the output of the model. The term LL, in the nonideal section, is the leakage reactance of the modeled transformer. This term arises because of the imperfect magnetic coupling between the primary and secondary windings. Term L, the magnetizing inductance, is larger than LL and appears as a shunt element in the transformer's model.

In Fig 2b, the term K represents the coefficient of coupling.

K= M/√LPLS

The primary inductance and the coefficient of coupling define the magnetizing inductance.

L=k2LP.

Eq 1 represents the leakage inductance, LL is

L1=LP(1-k2)(1)

This representation of the leakage inductance is convenient. Using an inductance meter, you can easily determine leakage inductance by measuring across the primary with the secondary winding shorted out. Shorting out the secondary's inductance also effectively shorts out the primary's magnetizing inductance, leaving only the leakage inductance.

In Fig 2b, the reciprocal of the turns ratio for the transformer's model is

a=k√LP/LS

For the case of the ideal transformer, the coefficient of coupling is unity. As a transformer's characteristics approach this value, its magnetizing inductance, L, becomes approximately equal to its primary inductance, LP, and the ratio 1/a, therefore, approximates the turns ratio, n.

This model assumes that the transformer's core is both linear and lossless. These assumptions are a good approximation for most low-power pulse transformers. The model also assumes that the resistance of the wire that winds the transformer is much smaller than either RS or R'ST Consequently, the model omits this term.

Only distributed capacitive elements can accurately model the capacitance of the transformer. But such elements would make the analysis intractable. However, for transformers with a turns ratio of unity or greater, you can make good approximations. To do so, realize that the secondary's capacitance predominates over the primary's capacitance. Thus, a single lumped capacitive element, in shunt with the transformer's secondary, can approximate the transformer's distributed capacitance. In many practical cases, the capacitance of the load is greater than this transformer's shunt capacitance, and the load capacitance is then the dominant term.

If you need a more detailed analysis of the transformer's distributed capacitance, perform a Spice simulation starting with the basic model this article presents and add the appropriate capacitive elements.