Pulse-Density Modulation: What Analog Should Be
Anyone who follows my columns knows that I am a big advocate of Delta Sigma Modulation (DSM) and signal processing in the density domain. It has frustrated me that many engineers have considered using the DSM, but only as the front half of some black box ADC. Lately, I have been encouraged by a series of products that convert an analog input into a one-bit digital density stream. Most microcontroller-based systems that I have designed have required some analog circuitry to buffer a signal, amplify its amplitude, and filter its bandwidth. Sometimes the signal has to be isolated or extracted from a very high common mode. After all this work, the signal is ready to be digitized. Care has to be taken to make sure that this processed signal does not pick up addition noise on its way to the ADC. This may require guards or shields to isolate the signal from noise (digital or power) contributors. In general, it’s better to just convert the signal to a digital stream and forego all this grief. Below is a schematic for a simple amplifier and filter.
Figure 1 Acquiring an analog signal may require amplifying and filtering a raw input signal.
Here, the gain is set by the ratio of the two resisters while the bandwidth is set by the feedback capacitor and resister values as shown in the equation below.
Where a filter feeds back the analog output, a delta sigma modulator feeds back the quantized output. This is shown in the figure below.
Figure 2 Feeding back the quantized output makes a filter into a delta sigma modulator.
Now the digital output is high if the signal is positive and low if negative. The output of the comparator can be thought of as taking the signal and adding a quantization error (eq) to it. With this in mind, the result of this is shown in the equation below.
In this way, the information is available in the digital stream and can be recovered with digital filters to reduce the quantization error. Fortunately, as the equation shows, this error has been high passed and the error has been pushed into the higher frequencies. This makes it easier to filter.
These filters can be implemented with a DSP, programmable logic, or even a microcontroller. If implemented with logic, a popular filer to use is a SINCN filter. This is a FIR filter that requires no multiplication, just adds and subtracts. In a previous column, I showed how to construct one with only a subtractor.
I bring attention to this MEMS microphone from Akustcia because of their understanding of DSM. I have taken the block diagram from their product brief and shown it in the figure below.
Figure 3 A Pulse Density Modulator at its basics.
Note that they call the digitizer, following the preamp, a modulator instead of an ADC. It is, in fact, a 4th order delta sigma modulator. In their brief, they state:
The AKU440 employs Pulse Density Modulation (PDM) for data output, a single-bit digital stream…
They consider the data to be a density stream that can processed downstream by whatever device requires this data. If the microphone needs to be isolated, this can be done with either optical or capacitive isolators. This is far less expensive than using analog isolators.
I have three issues with their product. The first is that they call it a Sigma Delta Modulator. Purists know the correct name is Delta Sigma Modulator. This may seem as trivial as Gulliver’s big Enders and little Enders, but hey, we all have our idiosyncrasies.
The second is that the clock is brought in as an input. I would have preferred a built-in resonator and have the clock embedded into the design stream, thus eliminating a pin. Actually, it is possible to process the signal without the clock. The clock just removes any level transition delay errors.
The third is that instead of a multiplexed output, I would have preferred L+R and L-R output density streams. This would allow for the select input to also be removed. The microphone would now only have power and output connections. This would make it easier to isolate and control. Hook up the power and data just flows. The L+R output allows for mono use while the two signals can be easily processed to generate left and right channels. I showed a simple way to do it in one of my previous columns.
A Great Product Waiting to be Built
Electric cars have battery packs that can be 100s of volts. With lithium cells having a 3.3 nominal voltage, a great many cells are going to have to be stacked in series. Efficient charging requires charge load balancing and to do this requires measuring the voltage across each cell. These are 3.3V nominal signals you would like to measure with a resolution of 1mV to 10mV. The high voltage and high common mode make this difficult to do conventionally. The figure below shows a pulse density modulation approach:
Figure 4 A Ratiometric DSM makes measuring stacked battery voltages inexpensive
A Ratiometric Delta Sigma Modulator is connected to a reference. The density output will be the ratio of the reference voltage and the supply voltage. As the battery voltage decreases, the density increases. There is no common mode problem because each chip sits directly across its battery and sees no more than 3.5V. The data output can be capacitor coupled to level shift the signal to the measure system that will process the signal. This measurement needs resolution somewhere in the range of one part in 330 to one part in 3300, or about 8 to 10 bits. This should be able to be implemented with a 1st or 2nd order modulator. The resulting circuit doesn’t require much silicon and it fits in a very small three-pin package. I can see a time that every battery will have one installed and sold as “PDM-enabled”
A modulator is a device that converts an analog signal into a digital density stream. It is a block that is as fundamental as the D- flip-flop and should be as well understood and as commercially available. I believe that as engineers use them, they will be better understood and more products will become available.