Pulse Forming Networks (PFNs) are used to generate output pulses which approximate a square wave shape. In their simplest form (e.g. Rayleigh lines), the use of an array of equal inductors and capacitors are used to approximate a transmission line with discrete elements. In other forms, the component values are optimized to synthesize a pulse output with minimum flattop ripple. In the examples below, 5 section PFNs are shown. PFNs with fewer sections can also be designed although they would typically generate more pulse ripple and longer pulse risetimes/falltimes. Since PFNs approximate a transmission line, they must be charged up to twice the desired output pulse voltage since half the voltage is dropped across the PFN impedance and the remainder across the load impedance.

Each of the following waveform plots can be clicked on to open up the full size graph in a separate window.

Significantly more detail on PFN synthesis and design can be found in Chapter 6 of the book Pulse Generators by G.N. Glasoe and J.V. Lebacqz, published by McGraw Hill, New York in 1948.

Type A PFN

The circuit schematic for the Type A Pulse Forming Network is shown below. Type A PFNs are sometimes used with high voltage Marx banks acting as the primary capacitance (the capacitor on the far left of the schematic). The primary capacitance is initially charged and all other capacitances are uncharged. In this specific model, the primary capacitor has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Type B PFN

The circuit schematic for the Type B Pulse Forming Network is shown below. In this Type B PFN, each capacitance has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Type C PFN

The circuit schematic for the Type C Pulse Forming Network is shown below. In this Type C PFN, each capacitance has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Type D PFN

The circuit schematic for the Type D Pulse Forming Network is shown below. One advantage of the Type D PFN is that each section capacitance is equal, making the design and procurement simpler. However, although the Type D PFN is mathematically possible, realistic implementation is not because of the negative inductance values in series with each capacitor which are not physically realizable. For discussion purposes, we will still examine this case. In this Type D PFN, each capacitance has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Type E PFN

The circuit schematic for the Type E Pulse Forming Network is shown below. Type E PFNs are based upon the Type D PFN model but have been modified to allow realizable construction. The negative series inductances have been replaced with a set of mutual inductance values, making the algebraic sum of the inductances around each mesh the same in both the Type D and Type E designs. In many cases, coils can be wound on a single tubular form and their spacing adjusted in order to adjust the mutual coupling. In this specific model, each capacitor has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Type F PFN

The circuit schematic for the Type F Pulse Forming Network is shown below. With the Type F PFN, the primary capacitance is the capacitor on the far right of the schematic (in this case, the 0.456T/Z value) and is initially charged up while all other capacitors are uncharged. In this specific model, the primary capacitor has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

Rayleigh Line PFN

The circuit schematic for the Rayleigh Line Pulse Forming Network is shown below. Rayleigh Line PFNs are often used since they approximate a discrete element transmission line. The circuit capacitors and inductors are all equal values. Capacitor values are equal to the pulse duration divided by the product of the line impedance and the number of sections. The inductor values are equal to the product of the pulse duration and impedance divided by the number of sections. Each capacitor has an initial condition voltage of 1000 V. For our example simulation, we have selected a pulse width (T) of 10 ms and a load impedance (Z) of 100 ohm. A switch is closed at approximately time 0 and the PFN discharges into the 100 ohm load impedance (resistor).

The circuit schematic and waveforms below show the individual capacitor currents for the 5 section Rayleigh Line Pulse Forming Network. For our example simulation, we use the same component values and initial conditions as above.