In today’s highly competitive electronics environment, designers are constantly looking for ways to reduce overall system costs. One of the most commonly asked questions analog specialists at digital microcontroller (MCU) companies hear from customers is, is the almost costfree PulseWidthModulation (PWM) DigitaltoAnalog Converter (DAC) good enough for my application or do I need a higherperformance, standalone DAC, instead?”
The generation of an analog voltage using a digital PulseWidthModulated signal is known as a PWM DAC. As most designers’ PCB boards have a microcontroller with a builtin PWMoutput feature onboard, a simple digitaltoanalog data conversion can be easily realized by adding a few passive components at the MCU’s PWMoutput pin, as an alternative to using a standalone DAC.
However, in the MCU application environment, system designers can have DAC functionality nearly free of charge. PWM DACs are widely used in very lowcost applications, where accuracy is not a primary concern. Standalone DACs, however, are used for applications requiring higher accuracy.
Although the PWM DAC can be realized with the simple addition of a few passive components, implementing a PWM DAC for system applications is not a simple task. There are many limitations associated with this. Understanding the complexities of using the PWM DAC and its effects can save significant development time and effort.
This article presents a technique for converting a PWM pulse to an analog voltage using a simple RC lowpass filter. It also reviews the PWM DAC’s limitations and its key design constraints with regard to resolution, frequency, ripple, settling time and current consumption, which are very important design parameters that are largely affected by the resistor (R) and capacitor (C) values, as well as the PWM duty cycle and frequency.
Standalone DACs
Figure 1 (in gallery below) shows an example of a standalone DAC. Its analog output voltage is given by:
Where D_{n} is the digital code. For example, with a 12bit DAC, the user can get V_{out} = 2.5V with V_{ref}= 5V and D_{n} = 1,00000000000. Typical standalone DACs provide good linearity and a short settling time, which is the time required to update each output voltage.
How PWM DACs Work
Figure 2, below, shows a basic configuration of the PWM DAC. The MCU outputs a PWM signal to an RC low passfilter. The PWM pulse train’s digital value becomes an analog voltage, when it passes through the RC filter. At a given period of time, the analog output is proportional to the PWM pulse’s high durations.
A PWM signal is defined as a digital signal with a fixed frequency, but a varying duty cycle. Figure 3 illustrates a PWM signal. The PWM period (T) is the time interval required to complete one full PWM cycle. The duty cycle is the ratio of the high duration (t) to the total period (T).
The PWM signal and RCfilter circuit parameters affect the analog output’s resolution, amplitude, settling time and ripple. The PWM DAC’s limitations are clearly demonstrated by analyzing the interaction of the PWM parameters and the RC filter. A better understanding of the relationship between these parameters enables designers to optimize the PWM to best suit their application’s requirements, while minimizing design time.
PWM DAC Bit Resolution
The PWM counter length (L) and the smallest dutycycle change in the PWM counter (C) determine the PWM DAC’s bit resolution. The following equation expresses the maximum bit resolution of the PWM DAC:
Where:
R = Resolution in Bits
L = Length of Counter in Bits
C = Smallest DutyCycle Change
For example, if the system generates an analog output voltage from a PWM DAC with a counter of 4,096 (L) and a minimum count step of one (C), the PWM DAC’s bit resolution is 12 bits.
When the PWM resolution is determined, it is possible to calculate the Least Significant Bit (LSB) size. The LSB size is dependant upon the PWM resolution and the PWM’s outputhigh level voltage (V_{OH}) and can be calculated using the following equation:
For example, a 12bit PWM DAC with a V_{OH} of 5V has an LSB size of 1.2 mV.
RCFilter Design Considerations for PWM DACs
One key design consideration when determining the PWM’s resolution is outputvoltage ripple. Ripple occurs due to overshoot and undershoot as the PWM charges and discharges the RC circuit. One way to approximate the charge characteristics is to modify the equations to charge and discharge an RCfilter circuit. As the effects of this are cumulative, the following equations can be used as approximations:
V_{LH} is the voltage increase for a specific PWM period and V_{HL} is the voltage decrease for a specific PWM period. The values of V_{LH} and V_{HL} are dependant upon not only the RCfilter values, but also upon the PWM frequency and duty cycle. The PWM frequency and duty cycle determine the time available for the PWM to charge (t_{charge}) and discharge (t_{discharge}) the capacitor. V_{ripple} is the difference between V_{LH} and V_{HL} for the same PWM period.
Figure 4 illustrates the magnitude of the voltage ripple across the output capacitor versus time. The vertical axis displays the magnitude of the ripple voltage, while the horizontal axis provides the corresponding time. The plot shows how the ripple voltage settles at approximately 125 mV in a time interval of approximately 40 ms for R = 10KO and 250 mV at 20 ms for R = 1 KO. In the previous example, an LSB size of less than 1.2 mV for a 12bit system was needed. This ripple is greater than 100 LSB for a 12bit DAC with a 5V reference, meaning the resulting PWM DAC solution has an effective resolution of less than 6 bits due to the ripples.
The ripple can be reduced by increasing the capacitor and resistor values or by increasing the PWM frequency.
As shown in Figure 4, the ripple decreases as the resistance value increases. However, nothing comes without a price — settling time doubles as the ripple decreases by 50 percent.
For applications that require faster settling time (increased bandwidth) and higher resolution, a second RC filter can be added. Obvious tradeoffs include the cost of additional components and the increased board space occupied. Figure 5 shows a model for a twopole RC lowpass filter. Figure 6 shows the analogoutput voltage of this model.
There are a couple of things to keep in mind when designing the filter. First, make sure the RC pole is set at a much greater frequency than that of the signal being generated. Secondly, if you are designing a twopole filter, make sure that R2 > R1.
The 3dB corner frequency of the RC filter is given by:
There are a couple of additional things to consider. Increasing the PWM frequency will also decrease the ripple, but the tradeoff is increased settling time. Figure 7 shows this case for 10 MHz and 5 kHz.
The worstcase ripple occurs at a 50 percent duty cycle. The ripple will decrease as the duty cycle moves closer to 0 or 100 percent. Figure 8 shows the peaktopeak magnitude of ripples on the PWM DAC output. The ripple decreases almost two times as the duty cycle changes from 50 to 85 percent.
V_{OH} = 5V, C = 10 µF, R = 1 kO, PWM Frequency = 1 kHz, Duty Cycle = 50 percent (Solid Curve) and 85 percent (Dotted Curve).
PWM DACs and Power Consumption
Many electronic products today are portable or handheld devices. These devices are batterypowered and many have strict constraints with regard to power consumption. Therefore, it is a good idea to minimize the PWM DAC’s power consumption. The current consumed in the PWM solution is simple to approximate, using the following equation:
Figure 9 shows the current and voltage plots. As shown in the plot, the PWM DAC with a lower resistor draws a significant amount of current (in the range of a few mA). This high level of current consumption is unacceptable for many batterypowered applications. Current can be decreased by increasing the resistor value.
In Figure 10, the resistor value has been increased by a factor of 10, which has likewise decreased the current consumption by a factor of 10.
As the resistor limits the current available to charge/discharge the capacitor, decreasing the amount of current available (increasing resistance) to the circuit will increase the settling time.
Another factor to consider is the filter’s pole. As the resistor value increases, the 3 dB frequency decreases by the same magnitude. This can be compensated for by reducing the capacitor value by the same magnitude, which offsets the increased settling time and maintains the original pole of the filter. Figure 11 demonstrates this. Note that, as the capacitor value reduces, the circuit becomes more susceptible to loading. This is another important design consideration.
Conclusions
Although the PWM DAC is simple and lowcost, using it to generate a stable analog voltage output is not a simple, straightforward task. Various design constraints must be considered and understood before realizing the circuit. In some cases, the design steps become very timeconsuming and tedious work for busy system designers.
The limitations associated with PWM DACs are low bit resolution, slow settling time, poor power efficiency and timeconsuming design steps, when compared to standalone DACs.
PWM DACs can be used for lowcost, low resolution (less than 10bits) and very low frequency applications (less than 1 kHz) where power consumption is not a critical parameter. On the other hand, a standalone DAC should be considered when high accuracy, short settling time, low power consumption and short design cycles are needed.
Author Information

Youbok Lee, technical staff engineer with Microchip Technology’s Analog & Interface Products Div., has more than 20 years of industry experience in RF, embeded circuits and remotesensing applications.

John Austin is the senior products marketing manager with MicrochipTechnology’s Analog & Interface Products Div.
