Archive for December, 2015

Still More Fun With Direct Digital Synthesis: TeensyLC with DAC

I posted a link to my previous page on setting up PWM Direct Digital Synthesized sine waves on PJRC’s Teensy 2.0, a 32u4 Arduino. Paul Stoffregen (the PJ in PJRC) commented that I should try porting my DDS demo sketch to a TeensyLC. “You won’t need PWM” he said. “Use the Digital Analog Converter” he said. I was a bit hesitant because TeensyLC has an ARM processor running at 48 Mhz. Quite a bit more power than the Atmel 16 Mhz chips and more I/O capability, so worth a look.  PJRC supplies an Arduino IDE add on called Teensyduino which configures support for PJRC boards so simply doing an analogWrite to pin A12 (took me a while to actually find A12) starts the DAC instead of starting PWM. Teensyduino has an included library IntervalTimer which sets a repetitive timer running and attaches that to an Interrupt Service Routine which you supply.  So an LC port should be simple as the dirty work of configuring the timer is taken care of.

Arduino PWM based DDS uses a fixed sample rate of 31 or 62 Khz and the interrupt generated sine wave has to fit into that constraint. That means low frequency audio tones are relatively smooth as there are lots of sample periods to go around even with the 256 step tables. High audio frequencies on the other hand, suffer distortion as the shorter period audio wave can’t fit in enough sample periods.

In the TeensyLC, the DAC always gets a fixed number of bits so you change the interrupt frequency to change the frequency of the generated audio tone. For instance, using the 256 step table, to generate a 1000 Hz tone requires 1000 * 256 interrupts per second. That’s about one every four microseconds, which even with the 48 Mhz processor clock, is going to use a LOT of CPU time. The shortest period I could set with IntervalTimer was 5 microseconds, my experiments with the demo program showed a maximum audio frequency of 650 Hz with the 256 step table, the 128 table limited at 1300 Hz, and the 64 step table maxed out at 2600 Hz.

Another down side to the DAC method stems from the fact that the audio frequency granularity is determined by the 1 microsecond granularity of the IntervalTimer function multiplied by the number of steps in the sine table.  The demo program shows this while sweeping. Low audio frequencies sweep smoothly but the higher frequencies have very noticeable jumps. Higher sine table sizes show this effect much more.

But the output wave form is much better than PWM. The following photos were shot using the Quarter Wave symmetry version of the demo sketch. Full table version traces were identical. All these were taken at a set audio frequency of 440 Hz. The filter was a single 10K resistor in series with the output pin, and a 0.01 ufd capacitor to ground. You can see the wave period changing a bit with the different table sizes. That is due to the granularity issue.

TeensyLC DAC Bottom - Raw, Top - Filtered 256 Step Table, Quarter Wave

TeensyLC DAC Bottom – Raw, Top – Filtered
256 Step Table, Quarter Wave

 

TeensyLC DAC Bottom - Raw, Top - Filtered 128 Step Table, Quarter Wave

TeensyLC DAC Bottom – Raw, Top – Filtered
128 Step Table, Quarter Wave

 

TeensyLC DAC Bottom - Raw, Top - Filtered 64 Step Table, Quarter Wave

TeensyLC DAC Bottom – Raw, Top – Filtered
64 Step Table, Quarter Wave

 

TeensyLC DAC Bottom - Raw, Top - Filtered 32 Step Table, Quarter Wave

TeensyLC DAC Bottom – Raw, Top – Filtered
32 Step Table, Quarter Wave Symmetry

 

TeensyLC DAC Bottom - Raw, Top - Filtered 16 Step Table, Quarter Wave Symmetry

TeensyLC DAC Bottom – Raw, Top – Filtered
16 Step Table, Quarter Wave Symmetry

I will probably use the TeensyLC in my next version of morse keyer.  I have to find a 16×2 LCD that will work at 3.3 volts, figure out how to interface a 5 volt PS2 keyboard, and how to charge and connect a 5 volt battery pack. The LC (and the 32u4) have USB serial built in which will make interfacing a terminal window on a logging computer a lot easier.

I found a useful web page showing how you implement quarter wave sine symmetry DDS on an FPGA and I took this opportunity to streamline the quarter wave ISR. You have to be familiar with bit banging to understand it now.

The demo sketches, full table and quarter table versions, and the Libre spreadsheet I used to develop the quarter wave half step offset tables are included in the archive at:
https://dl.dropboxusercontent.com/u/40929640/ArduinoSineSynth/TeensyLC_DDS_Demos.zip

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More Fun With Direct Digital Synthesis: 32u4 and Fast PWM

32u4 Port

My 2015 winter project will be an expanded version of the Morse Code keyer I built last year. I now have a PJRC Teensy 2.0 controller board (from Sparkfun) to use. The Atmel 32u4 based Teensy 2.0 is even smaller than the Pro Minis I have been using. It is attractive because it has USB built in for program loading and serial transmission. And there’s lots of I/O pins available which will make an LCD easy to connect. I note that everybody making a 32u4 “Arduino” is defining a different pinout from the chip. The Adafruit Feather is quite ambitious, has it’s own IDE addon and can be bought with Bluetooth or WiFi  included.

This breadboard photo shows the Teensy 2.0 at top left, Sparkfun Pro Mini at center, Sparkfun RedBoard top right, and a MicroCenter Pro Mini clone at bottom right.

Arduinos

 

PJRC has ported many of the standard Arduino libraries to their 32u4 Teensy form factor and these are included in your Arduino IDE when you download and install the Teensyduino addon. But my keyer sketch uses Direct Digital Synthesis to form a nice sine wave side tone which requires direct setup of a Pulse Width Modulation timer inside the AVR chip. My implementation is based on code from Jeff Whitlatch, KO7M.  I used timer 2 in last winters UNO based keyer as that’s the timer that does tone() in the Arduino UNO and I completely superseded that function. Reading the data sheet on 32u4 shows that it doesn’t even *have* a timer 2. It has timer 0 (8 bit), timers 1 and 3 (16 bit), and timer 4 (10 bit). Digging into the Teensy Arduino libraries shows that PJRC is using timer 3 for tone() so I needed a port that just changed the timer used. Comparing the 32u4 data sheet with the Mega328 data sheet showed that the only difference besides the timer number would be in the Waveform Generation Mode bits. 32u4 has four WGM bits, Mega328 has 3. I used a mode setting that turns the 16 bit 32u4 timer 3 into an 8 bit timer and Success! The port was working in my test program.

Fast PWM

Phase Correct PWM in an AVR processor uses the timer in a manner that has it count from 0 to 255 then count back down to zero for each interrupt cycle. The PWM signal goes high on the way up and low on the way down. For an 8 bit counter, that’s 510 counts per cycle (read the data sheet to find out why it skips two) so with no clock scaling the sample rate is 16 MHz/510 or 31.4 KHz. In Fast PWM mode the timer counts from 0 to 255 then rolls over back to zero. A PWM wave on the output pin goes high on the way up and low on overflow. This results in some jitter on the PWM pulses but the sample rate is twice as fast, 16 MHz/256 or 62.5 KHz. I decided to try Fast PWM in the test program. It required only a change in the math that calculates the sample rate, and a slightly different set of WGM bits.

The following images show comparisons of the 31.4 KHz (Phase Correct) and the 62.5 KHz (Fast) rate tone waveforms from the test program. The PWM signal is filtered by a single 10k resistor and a 0.01 ufd capacitor to ground at the scope connection.

Comparison of Phase Correct PWM with Fast PWM

Comparison of Phase Correct PWM with Fast PWM at 100 Hz

 

Comparison of Phase Correct PWM with Fast PWM at 1000 Hz

Comparison of Phase Correct PWM with Fast PWM at 1000 Hz

 

Comparison of Phase Correct PWM with Fast PWM at 5000 Hz

Comparison of Phase Correct PWM with Fast PWM at 5000 Hz

 

Comparison of Phase Correct PWM with Fast PWM at 10000 Hz

Comparison of Phase Correct PWM with Fast PWM at 10000 Hz

 

There is a clear improvement at the higher sample rate in the amount of “fuzz” on the waveform. The fuzz is at the sample rate and is the result of the 0.01 ufd capacitor integrating the PWM square wave. At twice the rate, the capacitor has half the time to charge or discharge. You can see at 5 KHz, the Fast PWM signal is much closer to a sine wave than Phase Correct. At 10 KHz, both are falling apart. A better output filter that cuts off the sample frequency would help but for morse keyer side tone from a tiny speaker, the average amateur radio operators ear won’t know the difference. I may try a switched capacitor filter some time in the future just to see. Watch this space.

Revision History

2015/12/08   The photos above are all from the 32u4 port. The program uses quarter wave symmetry to reduce the table size by a factor of 4. Two sketches, one running on UNO or other Mega328 controllers, the other for the PJRC 32u4 Teensy are at:
https://dl.dropboxusercontent.com/u/40929640/ArduinoSineSynth/Quarter_Wave_Demos.zip

I also back ported the changes to an earlier sketch that did not take advantage of symmetry. Scope traces were identical to the 32u4 port. Since the complete 360 degree cycle is specified, the code may be modified to generate arbitrary non-sinusoidal waveforms by manipulating the tables. Download at:
https://dl.dropboxusercontent.com/u/40929640/ArduinoSineSynth/Full_Table_Demos.zip

Each of these zip archives has a copy of the spreadsheet I used to construct the sine tables.