PWM Multipliers

The PWM multiplication method uses an ideal buck converter and a filter to multiply two time-varying signals. The buck converter transfer function is:

\[ V_{OUT} = duty cycle \times V_{IN}\]

The two input signals are mapped into the buck converter's inputs ???MATH???V_{VIN}???MATH??? and $duty cycle$. In order to make this mapping, the maximum amplitude of the input signal which is mapped to the ???MATH???duty cycle???MATH??? input needs to be known. In the following expression, the ???MATH???V_A???MATH??? input is mapped to the ???MATH???duty cycle???MATH??? input and the ???MATH???V_A???MATH??? input has a known maximum voltage of ???MATH???V_{AMAX}???MATH???.

\[ V_{OUT} = V_{AMAX} \times \frac{V_A}{V_{AMAX}} \times V_{B} = V_A \times V_B \]

Finally, an output filter is required to remove the switching ripple. The filter type, number of poles, and pole location are up to the user.

Advantages:

  • High precision at low frequencies. The idealized buck converter which uses the Switched Voltage-Controlled Voltage Source has no losses and can the transfer funtion is exactly the theoretical buck transfer function of ???MATH???V_{OUT} = duty cycle \times V_{IN}???MATH???.
  • Compatible with the POP and AC analyses

Disadvantages:

  • Poor high frequency performance. The output of a PWM multiplier is heavily filtered to remove the switching ripple, which leads to significant phase shift at low frequencies. This phase shift limits the multiplier to applications such as PFC converters where the maximum bandwidth required is in the kHz range.

PWM Multiplication Example

You can download this example here: 1.9_SIMPLIS_Multiplication.sxsch

This example uses the Switched Voltage-Controlled Voltage Source to create an ideal, loss-less buck converter. The buck converter output is then filtered with a four pole LC filter to get the DC value.

This example circuit also has a PWL Multiplier example and the error of each technique is plotted on the output graph.