Electronic – Difference between bit rate and baud rate and its origins

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.

USB - Universal Serial Bus - Signaling (WikiPedia)

The real problem with USB is not in the physical signalling. Say you capture a waveform with a scope right after the device is connected. It's likely to be a part of a Setup packet which is a part of a control transfer which is a part of a descriptor request which is a part of device enumeration, and that's only to have your device recognized by the host. Actual data transfer hasn't even started yet, and it will be wrapped inside transfers (of 4 different kinds) to some endpoint belonging to some interface that implements some device class, standard one like HID or completely custom. It's a lot like trying to understand HTTP by looking at Ethernet signal with a scope. In fact, you'd probably have a hard time finding your UART data even in a USB sniffer log (unlike a TCP/IP sniffer, a USB sniffer may well not know the exact protocol that e.g. FTDI uses to transfer data).

Together with the great USB in a Nutshell tutorial (HTML version), I found this book to be an excellent reference if you actually want working knowledge of USB to e.g. create your own USB devices.