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Suppose we have a PWM signal which controls the speed of a motor and a digital pin which specifies which direction a motor is travelling in, how can we convert these signals into 1 +/- 10V signal where <0 is reverse and >0 is forward travel.
I appreciate there will be several ways of implementing this, but it's be good to consider different methods
Something like this should work well. Parts are just for example, optimization will take more work (and information).
simulate this circuit – Schematic created using CircuitLab
Edit:
I've been asked for analysis of the amplifier (gain = +2 for switch closed, -2 for switch open).
First observe that the op-amp inputs are always at Vin/2 at balance due to R3/R5.
(Note also that they are always positive since Vin varies from 0V to 5V, so M1 always sees positive voltage on the drain- 0 to 2.5V for 0 to 5V in)
Switch M1 open (off), we have current (Vin - Vin/2)/R2 flowing through R2, so - (Vout - Vin/2)/R1 must be flowing through R1, using KCL.
Solve for Vout/Vin = 1/2 - R1/(2*R2) = -2.00 for R1 = 5*R2
With the switch closed (assume M1 = 0\$\Omega\$) we have an added term and using KCL again, the result is:
Vin/(2*R2) - Vin/(2*R4) + (Vout -Vin/2)/R1 =0
Solve for Vout/Vin = 1/2 +R1/(2*R4) - R1/(2*R2) = +2.00 for R1 = 5*R2 R4 = (25/40) * R2.
I can see an analog scheme there, which is cool, but one thing is bothering me. If you have direction signal in the system, are you sure, PWM is used to actually modulate speed/position/voltage, or it is used to generate frequency? I have seen several systems where people controlled stepper motors with direction signal and PWM signal, which was used for step signal. This is WRONG! Yet people do it.
In fact, the question hints that in certain system a pulse/direction drive was replaced with analog drive, and some kind of interface is required to stitch things back together.
If this is the case, no analog circuit will help. Because the information is not compatible- pulses are position, while analog command is current (well, normally, not always). And if this is the case, you need a digital device, FPGA or Microcontroller, that will capture the pulses, calculate current command value accordingly. In fact, it's one of the features of modern servo drives. It will probably have to close the loop- otherwise errors will accumulate quickly. So bottom line, if this is the case, rethink the system.
Here is a single-IC solution that gets you pretty close:
If you need to adjust the circuit manually, I suggest that you short R5 to make a voltage-follower and adjust R4 until a 50% duty cycle gives an output voltage of 0V.
We can also use some maths to find our ciruit relationships. In this circuit, adjusting R4 is really adjusting the voltage divider of R1 and R4 so that
$$(\frac{V1_{max}}{2} - V_{neg})\frac{R_4}{R_1 + R_4} - V_{neg}= 0$$
Assuming V1 = 3.3V and Vneg = 10V:
$$(\frac{3.3V}{2} - 10V)\frac{R_4}{R_1 + R_4} - 10V = 0$$ $$(11.5V)\frac{R_4}{R_1 + R_4} - 10V = 0$$ $$\frac{R_4}{R_1 + R_4} = 0.8696$$ $$6.67R_1 = R_4$$
Once you get your offset adjusted, start adjusting R5 up until 100% duty cycle gets you 10V and 0% duty cycle gets -10V. Again, you should be able to calculate this step:
$$V_{out,max} = GV_{in,max} $$
Where 'G' is the opamp circuit gain and Vin,max is the maximum voltage on V+ (or the PWM at 100% duty cycle). In an inverting amplifier,
$$G = 1 + \frac{R5}{R6}$$
From this point, you should be able to use substitution and arrive at suitable values for R5 and R6.
As some of the comments show, we need a little more information. I will assume here that you are using micro-controllers and that both your PWM and Digital output pins are operating at 0-3.3V. Here is the digital logic that you are first trying to implement:
PWM DIR | Output
1 0 | 1 (Forward Direction)
0 0 | 0 (Forward)
1 1 | 0 (Reverse)
0 1 | 1 (Reverse)
This represents XOR logic. So the easiest way to implement this would be to use a simple XOR IC, and a level shifter. Not really much of a need for a low pass filter if you are driving a motor as the coils in the motor will act as a low pass filter
