Electronic – Setting HSYNC and VSYNC registers

I know it's a bit late, but I've just got this sabe doubt. After looking around, I've come across this Microchip Doc that shows some examples.

First, we calculate \$\text{PR2}\$. From this formula,

$$ F_\text{PWM} = \dfrac{1}{(\text{PR2} + 1) \times 4 \times T_\text{OSC} \times \text{T2CKPS}} $$

we get

$$ \text{PR2} = \dfrac{1}{F_\text{PWM} \times 4 \times T_\text{OSC} \times \text{T2CKPS}} - 1 $$

where \$T_\text{OSC} = 1/F_\text{OSC}\$, and \$\text{T2CKPS}\$ is the Timer2 prescaler value (1, 4 or 16).

Therefore, if we want \$F_\text{PWM} = 20\text{kHz}\$, and choosing \$\text{T2CKPS} = 1\$, we get \$\text{PR2} = 249\$. We should choose higher values for \$\text{T2CKPS}\$ only if \$\text{PR2}\$ exceeds 8 bits (\$\text{PR2} \gt 255\$) for the given prescale.

Now we calculate the max PWM resolution for the given frequency:

$$ \text{max PWM resolution} = \log_2(\;\dfrac{F_\text{OSC}}{F_\text{PWM}}\;) $$

That gives us \$9.9658\$ bits (I know, it sounds weird, but we'll use it like that later).

Now, let's calculate the PWM duty cycle. It is specified by the 10-bit value \$\text{CCPRxL:DCxB1:DCxB0}\$, that is, \$\text{CCPRxL}\$ bits as the most significant part, and \$\text{DCxB1}\$ and \$\text{DCxB0}\$ (bits 5 and 4 of \$\text{CCPxCON}\$) the least significant bits. Let's call this value \$\text{DCxB9:DCxB0}\$, or simply \$\text{DCx}\$. (x is the CCP number)

In our case, since we have a max PWM resolution of \$9.9658\$ bits, the PWM duty cycle (that is, the value of \$\text{DCx}\$) must be a value between \$0\$ and \$2^{9.9658} - 1 = 999\$. So, if we want a duty cycle of 50%, \$\text{DCx} = 0.5 \times 999 = 499.5 \approx 500\$.

The formula given on the datasheet (also on the linked doc),

$$\text{duty cycle} = \text{DCx} \times T_\text{OSC} \times \text{T2CKPS}$$

gives us the pulse duration, in seconds. In our case, it's equal to \$25\text{ns}\$. Since \$T_\text{PWM} = 50\text{ns}\$, it's obvious that we have a 50% duty cycle.

That said, to calculate DCx in terms of duty cycle as \$r \in [0,1]\$, we do:

$$ \text{DCx} = \dfrac{r \times T_\text{PWM}}{T_\text{OSC} \times \text{T2CKPS}} = \dfrac{r \times F_\text{OSC}}{F_\text{PWM} \times \text{T2CKPS}} $$

Answering your other questions:

2) The resolution of your PWM pulse with period \$T_\text{PWM}\$ is

$$ \dfrac{T_\text{PWM}}{2^\text{max PWM res}} $$

3) Because CCPRxL, along with DCxB1 and DCxB0, determine the pulse duration. Setting CCPRxL with a higher value than \$2^\text{max PWM res} - 1\$ means a pulse duration higher than the PWM period, and therefore you'll get a flat \$V_{DD}\$ signal.

EDID is used, among other things, to query the monitor for the timings it would like. It isn't used to transmit any video information.

I guess it's been so long that no one remembers, but VGA monitors back in the day had adjustments for the image location on the CRT. You could move it left or right, up or down, or scale it horizontally or vertically. More advanced monitors had additional adjustments. These allow you to compensate for whatever timing was in use, whatever local magnetic field there might be distorting the picture, etc.

Of course, what these adjustments are doing behind the scenes is adjusting the timing parameters. They were necessary because the VGA signal doesn't explicitly say how much blanking time there is. As you've noticed, there are some general conventions, and the monitor can (through EDID) advertise support for particular timings, but there's no requirement that those timings are what will be sent to the monitor.

What you can do, and what LCD monitors that still have VGA interfaces do when you press the "auto adjust" button, is guess at what the blanking time might be simply by looking at the R, G, and B signals. These should be black for the blanking time, and probably they aren't black otherwise. Of course someone could be looking at a black screen, and this approach won't work.

Similarly, I don't think there's anything in the VGA signal that will tell you what the resolution is. You can guess at it by looking for the edges between pixels, and timing them, and this is again what LCD monitors do. But remember, VGA is an analog signal, designed to be displayed on an analog device. It has no concept of "pixels".