Cancel PWM DAC ripple with analog subtraction

-November 28, 2017

Every PWM DAC design needs analog filtering to separate the desired PWM duty-cycle-proportional DC component from unwanted AC ripple. The simplest of these is the basic RC low-pass filter, which gives a peak-to-peak ripple amplitude (for the worst case of 50% PWM duty cycle, where TPWM = PWM cycle time, and assuming RC > TPWM) of:

Vripple / Vfullscale = TPWM / 4·RC

 The obvious design tradeoff is that while any desired degree of ripple attenuation can be achieved by choosing a large enough RC product, settling time will correspondingly suffer. For example, if we (fairly logically) choose a definition for the settling band as equal to ripple amplitude, then…

Tsettle = RC·ln(Vfullscale / Vripple)

 = TPWM·Vfullscale·ln(Vfullscale / Vripple) / (4·Vripple)

 

The consequences of this relationship can be illustrated by the 8-bit case:

Given: Vripple / Vfullscale = 1/256; RC = 64·TPWM

Tsettle = 64·ln(256)·TPWM = 355·TPWM

which, even for a fairly speedy 32 kHz (31µs TPWM), predicts a positively glacial 11ms settling time.

Clearly, if settling time is a critical design parameter, we’ll need to do better and find a less simplistic filtering scheme. The extreme possibilities that lie in this direction are illustrated by my previous DI, Fast-settling synchronous-PWM-DAC filter has almost no ripple.

But not every application that can’t tolerate molasses-in-January 355·TPWM settling times need or can justify such a complex filtering solution. The Design Idea presented here addresses these middle-of-the-road applications. As shown in Figure 1, it augments the basic R1/C1 low-pass with an inverter, R2, and C2, which combine to negate and subtract (most of) the undesired AC component from the wanted DC signal, leaving a relatively clean analog output with settling time much less than a simple RC filter.


Figure 1  Waveforms & schematic of PWM DAC ripple canceller

 

But how pure is “relatively clean”, and how fast is “much less”? Setting R2=R1 and C2=C1, the ripple and settling time figures for the new circuit are: 

Vripple / Vfullscale = (TPWM / 4·RC)2

Tsettle = TPWM·ln(Vfullscale / Vripple)·(Vfullscale / 16·Vripple)1/2

 

Referring again to the 8-bit case (illustrated graphically in Figure 1):

Given: RC = 4·TPWM

Tsettle = 22·TPWM = 0.69 ms

with a 32 kHz cycle, it’s 16 times faster, with a squared ripple-amplitude ratio!

For many applications, this represents a very worthwhile tradeoff between a modest increase in circuit complexity and a significant increase in PWM DAC performance.

 

 —W. Stephen Woodward is one of EDN's most prolific and innovative Design Ideas authors, with dozens of contributions to his credit.

 

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