# Pulse Transformer Theory

**Operating Principles of Pulse Transformers**

Pulse transformer designers usually seek to minimize voltage droop, rise time and pulse distortion. Droop is the decline of the output pulse voltage over the duration of one pulse. It is caused by the magnetizing current increasing during the time duration of the pulse.

To understand how voltage droop and pulse distortion occurs, it is important to understand the magnetizing (exciting, or no-load) current effects, load current effects and the effects of leakage inductance and winding capacitance. The designer also needs to avoid core saturation and therefore needs to understand the voltage-time product.

The magnetic flux in a typical A.C. transformer core alternates between positive and negative values. The magnetic flux in the typical pulse transformer does not. The typical pulse transformer operates in a unipolar mode (flux density may meet but does not cross zero).

A fixed D.C. current could be used to create a biasing D.C. magnetic field in the transformer core, thereby forcing the field to cross over the zero line. Pulse transformers usually (not always) operate at high frequency necessitating use of low loss cores (usually ferrites).

**Figure 1A** shows the electrical schematic for a pulse transformer. **Figure 1B** shows an equivalent high frequency circuit representation for a transformer which is applicable to pulse transformers. The circuit treats parasitic elements, leakage inductances and winding capacitance, as lumped circuit elements, but they are actually distributed elements. Pulse transformers can be divided into two major types, power and signal.

An example of a power pulse transformer application would be precise control of a heating element from a fixed D.C. voltage source. The voltage may be stepped up or down as needed by the pulse transformer’s turns ratio. The power to the pulse transformer is turned on and off using a switch (or switching device) at an operating frequency and a pulse duration that delivers the required amount of power. Consequently, the temperature is also controlled. The transformer provides electrical isolation between the input and output. The transformers used in forward converter power supplies are essentially power type pulse transformers. There exists high-power pulse transformer designs that have exceeded 500 kilowatts of power capacity.

The design of a signal type of pulse transformer focuses on the delivery of a signal at the output. The transformer delivers a pulse-like signal or a series of pulses. The turns ratio of the pulse transformer can be used to adjust signal amplitude and provide impedance matching between the source and load. Pulse transformers are often used in the transmittal of digital data and in the gate drive circuitry of transistors, F.E.T.s, S.C.R.s, etc. In the latter application, the pulse transformers may be referred to as gate transformers or gate drive transformers. Signal type of pulse transformers handle relatively low levels of power. For digital data transmission, transformers are designed to minimized signal distortion. The transformers might be operated with a D.C. bias current. Many signal type pulse transformers are also categorized as wideband transformers. Signal type pulse transformers are frequently used in communication systems and digital networks.

Pulse transformer designs vary widely in terms of power rating, inductance, voltage level (low to high), operating frequency, size, impedance, bandwidth (frequency response), packaging, winding capacitance, and other parameters. Designers try to minimize parasitic elements such as leakage inductance and winding capacitance by using winding configurations which optimize the coupling between the windings.

Gowanda designs and manufactures pulse transformers in a wide variety of materials and sizes. This includes various standard types of “core with bobbin” structures (E, EP, EFD, PQ, POT, U and others), toroids and some custom designs. Our upper limits are 40 pounds of weight and 2 kilowatts of power. Our capabilities include foil windings, litz wire windings and perfect layering. For toroids, the list includes sector winding, progressive winding, bank winding and progressive bank winding. Gowanda has a variety of winding machines, including programmable automated machines and a taping machine for toroids. Gowanda has vacuum chambers for vacuum impregnation and can also encapsulate. To ensure quality, Gowanda utilizes programmable automated testing machines. Most of our production is 100% tested on these machines.

**Magnetizing (No-Load) Current**

Consider the simple pulse transformer circuit of **Figure 2A** and its equivalent circuit of **Figure 2B**.

There is no source impedance, winding capacitances, or secondary leakage inductance to worry about. With both switches open, there cannot be any primary or secondary currents flowing. Now close the primary switch. Since the secondary load is not connected, the pulse transformer’s primary winding acts like an inductor placed across a voltage source. Primary current begins to flow. This is the magnetizing current (no secondary current) and is governed by the differential equation V(t) = L x d(I)/dt + Rp x I(t), with units of volts, henries, amps, and seconds. If the power supply has constant voltage, Rp = zero, & L = Lkp+Lm is constant, the differential equation can be solved for I(t), I(t) = Io + V x t / (Lkp+Lm), where Io = the initial current which equals zero. Notice that the current increases at a linear rate over time and that the rate in inversely proportional to the inductance. The current flows through Np turns creating Np x I(t) amount of magnetizing force (amp-turns) which in turns creates a magnetic flux density in the pulse transformer core. Eventually the increasing primary magnetizing current would exceed the magnetic flux capacity of the pulse transformer core and will saturate the core. Once saturation occurs the primary current rapidly increases towards infinity (in theory). In a real circuit the primary winding resistance (and source impedance) would limit the current. See **Figure 3A** below for graphical illustration. For non-zero Rp, I(t) = I_{o} + (V/Rp) x e^{(-Rp x t / (Lkp + Lm))}. The effect of Rp is graphically illustrated in **Figures 3B** and **3C**. Rp extends the time it takes for the unloaded transformer (or an inductor) to saturate. If Rp is sufficiently large, it prevents the transformer (or inductor) from saturating altogether. Regardless of saturation, Rp places an upper limit on the primary current value.

**Voltage Droop**

For Rp = 0 the source voltage divides proportional across Lkp and Lm hence the voltage across Lm can be defined as Vm where Vm = V x Lm / (Lm+Lkp). The induced secondary voltage becomes equal to Ns x Vm / Np. For Rp > zero a voltage drop occurs across Rp. The value of this drop increases in value as the primary current increases with time, hence Vm decrease over time and consequently the secondary voltage declines over time. Thus Rp and magnetizing current contribute to secondary voltage droop. Lkp does not contribute to the droop in the no-load case but does contribute to a lower secondary starting voltage for both the no load and under load cases. Droop is graphically illustrated in **Figure 4B**. Compare it against the ideal pulse shown in **Figure 4A**. When a droop is present in the waveform, we do not get the consistent pulse wave amplitude as on the left.

**Voltage – Time Product**

Pulse transformers, being typically unipolar (D.C.) applications, require the primary switch to be opened (thereby removing the voltage source) before saturation occurs, whereas A.C. applications reversed the applied voltage before saturation occurs. Unipolar applications require that sufficient time be allowed to pass to re-set the core before starting the next pulse. This time permits the magnetic field to collapse (reset). The field does not completely collapse to zero value (unless forced to zero, or lower) because of core material remanence. A slight air gap may be used to bring remanence closer to zero value. The gap lowers the pulse transformer inductance. The flux range between remanence and the maximum flux is referred to as dB, the maximum change in flux density during the pulse duration, dt. The dB of the typical pulse transformer is less than half for that of an A.C. application because flux in A.C. applications can go from positive Bmax to negative Bmax. Operating frequency and maximum expected temperature affect the choice of maximum usable flux density value, Bmax. Saturation can be avoided by applying the following equation; dB x Np x Ac x Sf = V x dt x 100000000, where dt is the maximum time duration of the pulse, Ac is the core’s cross-sectional area and Sf is the core stacking factor ratio. Units are gausses, turns, square centimeters, volts and seconds. Be aware that dt does not include reset time, tr. Maximum operating frequency equals 1 / (dt + tr).

**Kickback Voltage**

In the foregoing discussion the primary switch was opened thereby interrupting the current flowing through the transformer primary. The resulting collapse in the magnetic field will induce a voltage reversal in the transformer windings. The more rapid the field collapse is, the higher the induced voltage. The transformer will try to dissipate the energy stored in its collapsing magnetic field.

If the transformer was under load, the induced voltage would cause current to flow into the load. In the no-load case of this example, the transformer does not have any readily available place to dissipate the energy. The transformer will generate the voltage necessary to dissipate the stored energy, hence a high voltage kickback (or flyback or backswing) voltage will occur in the windings. In a real circuit the transformer will induce eddy currents in its core thereby dissipating the energy as core loss. In a real circuit the high voltages can damage the switching elements (transistors, F.E.T.s, S.C.R.s, etc.). Many designs include protective circuitry across the primary winding.

**Secondary Load Current Effects & Rise Time**

Consider again the simple pulse transformer circuit of **Figure 2A** and its equivalent circuit of **Figure 2B**.

Initially, with both switches open, there cannot be any primary or secondary currents flowing. Close the secondary load switch and then close the primary switch. Current flows through the primary winding. The L x dI(t)/dt action induces a voltage in the primary winding which opposes the source voltage. A voltage, Vsi, is also induced in the secondary winding causing secondary current to flow. The ampere-turns created by the secondary current work against the induced voltage that opposes the source voltage. Consequently, the source voltage supplies more current flow through the primary. Currents rapidly increase until either the secondary current or primary current encounters a current limitation. Examples of such limits are the secondary load and winding resistances limiting the secondary current or the source impedance and primary winding resistance and primary leakage inductance limiting the primary current. Once a limit is encountered, an equilibrium is quickly established except for the magnetizing current. The primary current has two components: Irs, the load current transformed (reflected) to the primary winding and Im, the magnetizing current. As in the no-load case, the magnetizing current starts at zero and increases over time. The pulse transformer must be switched off before saturation occurs.

In this example the load is resistive, there is no secondary leakage inductance, and there is no secondary winding capacitance; hence a purely resistive load current is reflected to the primary winding. The primary current is larger than it was in the no-load case, hence more voltage drop is expected across the primary winding resistance. Consequently less voltage, Vm, is available across Lm which results in less induced voltage in the secondary winding. Secondary current flow through the secondary winding resistance causes another voltage drop hence lower transformer output voltage. Under load, both the primary and secondary winding resistance contribute to a lower secondary voltage. The secondary winding resistance does not contribute to pulse droop.

The reflected load current, Irs, does not flow through the mutual inductance, Lm, but does flow through the primary leakage inductance, Lkp. Lkp restricts the flow of the primary current (hence reflected load current also). Consequently the reflected load current cannot immediately reach its full value (nor can the secondary current). It is effectively delayed. Until the reflected load current reaches its full value, a larger voltage drop will occur across Lkp than there was in the no-load case. This larger voltage diminishes in value over time. Consequently Vm exhibits a time delay in reaching peak voltage value. This delay is also seen in the secondary output voltage. This delay is known as rise time. Rise time is graphically illustrated in **Figure 4B**.

**Effects of Winding Capacitance**

The circuit has all the components of the circuit in **Figure 2B**, but also has primary winding capacitance, secondary winding capacitance, core loss, and secondary leakage inductance. Start with both switches open and no capacitive energy and no inductive energy. All currents are initially zero. Close the secondary switch then close the primary switch. The primary leakage inductance, Lkp, restricts the flow of primary current by opposing the source voltage. The opposing voltage is generated by Lkp x d(I)/dt action. Current flow (from the source) finds the uncharged winding capacitance, Cp to be a much easier path, hence a relatively large amount of current flows into the winding capacitance. This large amount of current could be called a surge current because it will diminish over time as the capacitance is charged. The surge causes a relatively large voltage drop across the primary winding resistance, Rp, thereby initially lowering the voltage available to Lkp and Lm. Over time, as the surge current diminishes, the voltage drop across Rp diminishes, and the voltage across Lkp and Lm reaches full (peak) value. The surge effectively delays the peak voltage across Lm. This in turn delays peak secondary voltage. The delay contributes to rise time, hence Cp contributes to rise time. As discussed earlier, Lpk restricts flow of the reflected load current and consequently also contributes to rise time.A similar consequence occurs with the secondary winding capacitance, Cs. Any current supplied by induced secondary voltage must charge Cs as the secondary voltage tries to rise to peak value. This delays the secondary in reaching peak voltage, hence Cs also contributes to rise time.

TSecondary leakage inductance, Lks, restricts secondary current flow just like Lkp restricted primary current flow. Lks also delays the secondary peak output voltage, hence it also contributes to rise time.

TCore loss resistance, Rc, provides a relatively small current shunt path across Lm just like the reflected secondary load current does. It has the same effect but the effect is much smaller.

To summarize, winding capacitances and leakage inductances act to increase rise time. (They also generate trailing edges which is discussed later.) They may also contribute to spurious oscillations. In a typical pulse transformer design, core loss does not have much effect.

**Pulse Distortion**

Ideally the output pulse waveform should be identical in shape to the input pulse waveform except for a desired amplitude change due to the step-up or step-down turns ratio. Any other deviation is considered to be distortion. Rise time, droop, trailing edges, and spurious oscillations are all considered to be signal distortions.

**Figure 6A, 6B and 6C** illustrate various types of distortion. The trailing edge is further described below.

**Figure 6A** depicts an inductor that saturates, with no current limit. The following information is also relevant:

I_{m} = I_{0} + V_{p} x t/L

I_{0} = 0; R_{p} = 0; and L_{m} + L_{kp} = L

(referring to **Figure 2B** above)

**Figure 6B** depicts an inductor that does not saturate and is current limited. The following information is also relevant:

I_{m} = I_{0} + V_{p} x e^{(-Rp/L)t}/L

I_{0} = 0; R_{p} = 0; and L_{m} + L_{kp} = L

(referring to **Figure 2B** above)

**Figure 6C** depicts an inductor that saturates, but is current limited. The following information is also relevant:

I_{m} = I_{0} + V_{p} x e^{(-Rp/L)t}/L

I_{0} = 0; R_{p} = 0; and L_{m} + L_{kp} = L

(referring to **Figure 2B** above)

And the inductance L changes at I_{sat}

**The Trailing Edge**

For an ideal pulse transformer, once the primary switch is opened the secondary pulse should immediately end. This does not happen. The pulse transformer tries to dissipate the energy stored in Lm and in the parasitic components Cp, Cs, Lkp, and Lks. The inductance will induce voltages as their magnetic fields collapse. The capacitor charge will drain, but will not drain instantaneously. The capacitances may temporarily supply current to the inductances. As a result, there is a sloped decline of the secondary output voltage after the primary switch is opened. This sloped decline is referred to as the trailing edge. Some combinations of capacitance and inductance could produce spurious oscillations (known as ringing). A trailing edge is graphically illustrated in **Figure 6B** above.