Modeling of analog part for DDS3 signal generator

When building an AVR DDS2 signal generator, there were many discussions about signal conditioning in the analog part of the device. The first argument was that LM358 wasn’t the best choice for this purpose. Another one pointed to the sine wave that wasn’t smooth enough.

As you can see, there are some dents on it. Other waveforms also are distorted, especially when higher voltages are selected. This asks for a better analog part. Some people suggested replacing LM358 with OPA2134, but it seems to be quite an expensive choice. In my opinion, low noise, a general-purpose op-amp can be great too. I’m going to give a try to Texas Instruments TL074 low noise op-amp. It is low power, high slew rate (13V/us) IC – almost five times faster than LM358 and for the same reasonable price.

If we look at the DDS2 signal generator offset and gain control circuit, we can see a problem with it. We regulate offset before amplitude control – usually, offset should be adjusted after amplifying the signal. And the third problem is that offset can be handled in the small interval – in the 5V range, while we could do this in the -12V … +12V range. Let us redesign the analog part so it would give a better result.

Zeroing offset voltage

First of all, offset control, we can slightly modify the first stage so that the signal’s offset voltage would be set to 0. For instance, if we generate sine-wave on DAC, we get a maximum of 2.5V amplitude signal with a 2.5V DC offset. Instead of using POT1, we can calculate the resistor divider so that we get a 0V offset on the output. We assume that all signals coming out of the microcontroller have offset 2.5V (when VCC=5V), then we can model the following circuit:

Calculating is easy:

We know that the source voltage is Vs=2.5V. The output voltage is Vo=0V. We need a gain of 1 (-1 for inverting amp). So at inverting op-amp input, we get voltage:

From from operational amp analysis we know that V- = V+ and currents to both inputs are equal to zero (I- = I+ = 0A). Then We must get 1.25V at V₃. so we need to select a voltage divider to scale voltage from 5V to 1.25. To do so, we chose one fixed resistor value R3 to be 100kOhms, and then we calculate R4:

evaluate R4:

We can get 33.33kΩ by connecting two resistors in series: 33kΩ + 330Ω that will give the resulting voltage close enough to 0V.

Optional filter stage

In the next step of the analog part, we are going to add a filter. Since the DDS signal generator is capable of outputting various types of signals, we don’t want it to be hardwired. For instance, if we generate a sine wave, then we could use a filter to make it more smooth while on a square wave it would have a negative effect by rounding the shape. For this, we can add a bypass switch that would allow to insert or bypass filter on demand. What filter are we going to use for this purpose? Since we have plenty of op-amps on TL074, we can make an active filter.

I find Butterworth’s (Sallen – Key) low pass filter quite handy since it gives the band’s flattest response. Let’s select parameters for this filter. DDS generator, in our case, isn’t going to exceed 100kHz frequency. Also, we want attenuation in this up to roll-off frequency near 0dB. So let us increase the roll-off frequency up to 200kHz. This value we are going to use while calculating.

Resistor and capacitor values of the filter can be determined with these simple rules:

R1 = R2, C1 = 2·C2

If we select R2 = R1 = 33k (have plenty of these)

then we can calculate C2 as follows:

so standard value of C1 = 33pF.

You can check calculations online here.

DDS Signal amplitude gain control

After we have adjusted signal offset voltage filtered it (or not), the next part will adjust amplitude. We need to adjust the signal amplitude from 0 to 12V. For this purpose, we are going to use an inverting amplifier with an adjustable potentiometer gain. We need to calculate proper resistor values to get excellent gain control over all potentiometer turn. Say we are going to use a 47k potentiometer. Let us calculate the input resistor value.

Another known condition is that the input voltage from the previous stage is 2.5V. Say we want to get 12V amplitude on the output we need gain: 12/2.5 = 4.8. If we turn the potentiometer to the max left, we get:

R1=47k/4.8=9.79k~10k. To get 0V amplitude, we need to turn the potentiometer to the right, so the gain ratio gets close to 0.

Signal offset regulation

And the last stage of the analog part is signal offset regulation. We want to regulate offset in the range of -12V to 12V. The easiest way to do so is to add an offset voltage to signal voltage.

Since we already have two inverting cascades, we don’t want the last one to be inverted that would lead to an inverted signal on the output. So we are going to implement non-inverting summing:

Let us see how to calculate resistor values. R6 and R7 we select to be 100k resistors as they aren’t critical while in the recommended range of 1k to 1M. The more interesting part is the gain. Let us see how non-inverting summing amplifier output voltage looks like:

What we see here is a voltage added and multiplied by the gain. Since our R7 and R8 are equal to 100k, we get that only half of these voltages are added. So we need to adjust amplifier gain to 2 to operate with total values. So we need:

After solving we get that both resistors have to be equal. To keep resistor values less scattered we also chose those to be 100k.

Putting it all together

Now we have all blocks ready and can connect them into a single circuit:

Here we have linked all four modeled parts: offset adjust, low pass filter, amplitude control, offset control. TL074 chip comes with four operational amplifiers built-in to get away with a single chip and this functionality. If you are interested in simulating, here is the LTspiece simulation file. TL074 was replaced with a similar TL1359 op-amp in the simulator, so actual results shouldn’t differ much.

And corresponding signals on various nodes:

As you can see in the first stage, we have a sine signal with minor distortion added, and its offset is 2.5V. After offset adjusts signal still is distorted, but it crosses 0V now. After filtering, we see no more distortion – only smooth sine. Then next stage adjusts signal voltage gain, and on output, we get a signal with a selected offset somewhere at -5V. Results look promising, so the next step will be to put everything into a working project. Comments and suggestions are welcome.