What is Pulse Width Modulation?

How does pulse width modulation work? Referring to Fig. 1, the classical method of voltage mode PWM is to compare an error signal to a reference ramp oscillator waveform as shown in Fig. 1. In the figure, as the error signal crosses the rising edge of the ramp, the comparator output goes to its high output level, and conversely when the error signal crosses the falling edge of the ramp, the comparator switches to its low level output.

Also, if we wish the duty cycle to increase when the error signal falls, to correct the system output, or increase system output, such as the voltage of a regulated converter, or the speed of a motor, for example, the example of Fig. 1 shows exactly that effect. As the error signal drops, the pulse width increases, thereby applying more power, or voltage, or more signal level to the load.

Why do we convert the error signal to a PWM signal? Because the PWM signal can operate an electronic switch such as a mosfet or a transistor that will rapidly switch on and off and transfer power more efficiently. The comparator output, if it is 0 to 5 volts or higher, can drive the gate of a power mosfet directly thereby controlling a lot of power with a small signal. If needed, the output signal of the comparator can be buffered with a high current buffer pulse amplifier to allow the ability to drive very large transistor switches and even paralleled transistor switches for high power.

The Basic Buck Converter

A simple single switch buck converter is shown in Fig. 1. Because of the power loss in the diode D1, the single switch buck converter is not suitable for high current or high power applications. It would work, however, with suitable choice of components, for low power, low current, and low voltage applications. If the input voltage is less than 40 volts, D1 could be a Schottky diode to improve efficiency. Not shown in Fig. 1 is the method of developing the high frequency pulse drive signal which is usually a type of pulse width modulated (PWM) signal that drives Q1 either into a saturated-on condition of a fully turned off condition. As long as Q1 is either in the full on or full off state, alternately at the converter switching frequency, the power dissipation in Q1 will be relatively low as power is dissipated only during the times that current is flowing through the switch when voltage across the switch is not close to zero. There are some other losses in Q1 which are also present which we will discuss in another article.

We can define the duty cycle D at any given time as the ratio of the time the switch is on to the total time of the each switching cycle (also called the switching period.)

D = Ton / Tsw

The switching frequency can be constant or variable, but it is usually relatively constant under steady state conditions can be calculated as

Fsw = 1 / Tsw

The output voltage is set by the duty cycle and the input voltage under steady state conditions as

Vout = D*Vin = Vin * Ton / Tsw

The maximum or peak voltage, Vds, across the mosfet Q1, drain to source is

Vds = Vin + Vd

where Vd is the forward voltage of the diode. The function of the diode is to allow current to continue flowing to the load when Q1 is in the off state. The peak Q1 drain current is

Idrain = I_load + dIp_inductor / 2

where dIp_inductor is the peak inductor current above the DC load current and can be calculated as

dIp_inductor = Vin * Ton /L

where L is the inductance value in Henries. We note here that the capacitor C1 has to be rated to handle the ripple current from the inductor, and of course be rated for the output output voltage. If C1 is a tantalum capacitor, it is usually de-rated by 50% for the output voltage of the converter.

Finally, the diode average current can be computed as

Id = I_load*(1-D)

The diode has to be rated to handle the input voltage and its average current.

We have now covered the basic calculations for the single switch buck converter which would allow a power stage to be designed with selection of components for the application. We should also note that the buck converter is used only to reduce some input or bus DC voltage down to a lower DC voltage. We have not yet covered drive signal generation (PWM) for Q1 gate drive, nor the control network which is usually a feedback loop with frequency compensation elements.