Simcenter Testing Solutions Simcenter Testlab: Switching Frequencies and Pulse Width Modulation (PWM) Signals

Figure 1: By modulating the width of the pulses, a PWM signal can approximate a smoothly transitioning signal, such as a sine wave.
 

Pulse Width Modulated signals are used for a wide variety of applications. Applications include control valves, pumps, hydraulics, and heating elements. Sometimes a PWM signal is used as a sensor, where the width of the pulse is proportional to the amplitude a measured signal.

Another application for PWM signals is with power inverters. An inverter is a device that converts DC power to the AC power used to turn an electric motor as shown in Figure 2. 
 

Figure 2: An inverter in power electronics uses PWM signals to convert DC power to AC power.
 

For example, in an electric vehicle, the power inverter switches the connection between the battery and the electric motor on and off. Each switching event is a pulse. The inverter changes the speed at which the motor rotates by adjusting the timing between pulses and the width of the pulses as shown in Figure 3.
 

The pulses are varied to create a sine wave.  Because the electric motor has inertia.

A PWM signal consists of three main components that define its behavior: pulse width, carrier frequency and duty cycle. 

1.1 Pulse Width

The pulse width describes the amount time the digital output signal is “on”, or at the maximum value.  Some examples are shown in Figure 4. 
 

Figure 4: Pulse widths with varying "on" times.
 

Pulse width is measured in a unit of time and does not relate directly to the duty cycle or carrier frequency that will be discussed next.  However, as it will be shown, for a given carrier frequency the duty cycle and pulse width are directly related. 

Note that in these examples, the timing of the “on” event is the same, while the timing of the “off” is changed to vary the width.

1.2 Carrier Frequency 

The carrier frequency determines how fast the PWM completes a cycle (i.e. how fast it turns on and off). The period of the cycle (inverse of the frequency) is illustrated in Figure 5.
 

Figure 5: The carrier frequency of a PWM cycle is the inverse of the cycle time.
 

The frequency that the PWM signal needs to be set at will be dependent on the application and the response time of the system that is being powered.

Below are a few applications and some typical PWM frequencies.

1.3 Duty Cycle

The duty cycle describes the amount of time the signal is in an on state as a percentage of the total time of it takes to complete one cycle (see Equation 1 below).
 

Signals with the same period but differing duty cycles are shown in Figure 6.
 

Figure 6: Different duty cycles. The wider the pulse (top) the higher higher the duty cycle.
 

By cycling a digital signal off and on at a fast enough rate, and with a certain duty cycle, the output will appear to behave like a constant voltage analog signal when providing power to devices.

Example: 
To create a three volt signal given a digital source that can be either high (on) at five volts, or low (off) at zero volts, a PWM signal with a duty cycle of 60% can be used.  The PWM signal outputs five volts for 60% of the time. When the digital signal is cycled fast enough, the voltage seen at the output appears to be the average voltage. If the digital low is zero Volts then the average voltage can be calculated by taking the digital high voltage multiplied by the duty cycle: 5V x 0.6 = 3V

1.4 Switching Frequencies

When analyzing the noise and vibration behavior of a product that uses PWM signals, spectral content called "switching frequencies" are generated by the square wave pulses (Figure 7). 
 

The switching frequencies generated noise or vibrations are centered around the carrier frequency of the PWM signal.  They have several orders (the diverging lines in the picture above) around the carrier frequency.  These diverging (or converging) orders are caused by the changing of the pulse width.

2.  Simcenter Testlab and PWM Signals

The use of Simcenter Testlab to analyze Pulse Width Modulation (PWM) signals is covered in the next.  Getting started and the calculation of duty cycle and carrier frequency are covered.

2.1 Getting Started

If measuring the voltage pulses from a PWM signal from a sensor or controller, the Simcenter Testlab Time Signal Calculator or Virtual Channels feature in Simcenter Testlab Signature can be used to extract the carrier frequency and duty cycle.  

Postprocessing with Time Signal Calculator will be covered here, but the procedure is similar for virtual channels and online data:

2.3 Calculate Duty Cycle from PWM Signal

Calculating the duty cycle of a PWM signal is very similar to calculating the carrier frequency:
 

• Next press the “Calculate” button to perform the calculation.

• After saving the data (see previous section), the “Navigator” tab, can be used to visualize the duty cycle and original PWM signal time histories with an UpperLower display.

• To utilize offset order cursor, right click on colormap and choose "Add Single Cursor -> Order".

• Then double click on the order cursor. Type the carrier frequency offset into lower parameter box.

• Offset orders can also be specified in throughput processing. In the order section menu, there is an "Offset" field.