Electrical – Negative voltage PWM

When it is charging (input to the transistor low), it is charging towards 10V through a resistance of 6.45K ohms (the Thevenin equivalent source resistance of the divider plus the 4.7K resistor), and when it is discharging (input to the transistor high) it is discharging through a resistance of 4.7K ohms (to maybe 50mV- the VCE of the saturated transistor- it won't make much difference so I'll guess at it- you can refer to the datasheet for a slightly better value).

For steady state, assume the voltage is fixed (does not change during a cycle), so we know the current charging must equal the current discharging if the times are equal (ask if that is not obvious).

So (10 - Vc)/6.45 = (Vc - 0.05)/4.7

solving, Vc = 4.244V. (Even worse!)

I don't know where the value in your simulation comes from but there will be lot of ripple in the voltage with such a small capacitor. Figure about 0.001 second * 0.9mA/10^-6 = 0.9V, so +/-450mV ripple (about 10%), so perhaps it's the peak voltage, not the mean-> 4.244 + 0.45 = 4.694, which agrees with your simulation.

You can use a more symmetrical drive either by increasing the 4.7K to a much higher value or using a CMOS buffer that will also get rid of the Vce(sat) term. Just remember that the buffer does not make this issue magically go away, and if you have a relatively low resistance compared to the buffer output impedance, and that impedance is asymmetrical (as it usually is) you may not see the exact voltage you're expecting.

Note that using a highly asymmetric switch like this one introduces a significant nonlinearity, which may be undesirable. In this case, it's about -15% of signal at mid-scale or -7.6% of full scale.

If you really need to operate that slowly (usually faster is better, at least up to some kHz for PWM) then you have a couple choices- use a slower clock frequency (much lower, so maybe not desirable- but slower clock means less power consumption). It also does not give you fine resolution on the PWM period (because normally nobody cares that much as long as it is fast enough).

Or you can use the timer compare function to provide sub-microsecond accurate transitions since it can toggle the pin with the hardware compare function- you then set it up for the next compare (and, optionally, toggle the output pin). That would be the preferred approach, in my opinion.

Some of the 16F series parts have a numerically controlled oscillator peripheral (NCO), but I don't think it's available in the 18F series (could be wrong).