I've used Sabertooth and their sister SyRen controllers extensively. They are great quality devices, but they are NOT servo controllers. They are motor controllers, so they can change motor speed and direction, but they don't have feedback input and therefore cannot receive position commands.
The PWM signal is typically used in two ways:
- As low-current position control command for hobby servo controllers. In this case the width of a pulse defines target position and a servo moves motor to reach that position.
This has nothing to do with Sabertooth/SyRen controllers. They accept either analog or serial or R/C commands. You can convert your PWM signal into analog voltage (e.g. by using RC low-pass filter), which is cumbersome and imprecise, not to mention pointless. Or you can use mode 2 and send PWM signal at approximately 50-100 Hz frequency (not 10 kHz!).
In either case, your command will not control the position. It will only control motor speed and direction, even if you use R/C servo signal format. If you change the frequency of PWM in your MCU and configure the switches on Sabertooth accordingly you should be able to control the motor immediately.
- As high-current power to the motor. In this case the width of a pulse defines average current going through the motor and therefore direction and speed/torque. It is, indeed, typical for this signal to have 10-20 kHz frequency.
This kind of PWM is exactly what Sabertooth generates on its output. It does not require any PWM coming from MCU.
To answer you main question, the analog input is designed to receive stable (as in "not pulsed") DC voltage in a certain range. The simplest example would be a potentiometer between 5V and ground with wiper connected to analog input. Or, specifically in case of 2-channel Sabertooth controller, an analog joystick with its two axes connected to two analog inputs. This is exactly what Sabertooth is designed for, because it supports automatic mixing of these two channels into differential control of two wheels, also known as "tank" control.
Finally, analog signal is not the best way to control Sabertooth if you want to use it with MCU. Its main selling feature is support for a simple 1-byte serial protocol, as well as more advanced addressable protocol that allows connection of multiple controllers to a single UART port.
Having said that, you can build a servo driver using analog input. For this you need a sensor connected to the comparator circuit that generates analog command for controller. The comparator would compare sensor voltage (actual servo position) with analog signal from MCU (target position) and move motor to reduce the difference.
This is not a trivial task to design and tune up. And it would probably cost more than buying hobby servo of suitable size.