bjtfunction generatorsignal
I have two circuits that are supposed to be square wave to sawtooth wave converters:
Both circuits receive a positive square wave as their input and generate a positive sawtooth as their output. Do these circuits actually work? What are the modes of operation of the transistors? I need to know these in order to set up the equations for calculating the component values.
You are using the wrong topology for what you are trying to achieve. Here is a better circuit:
First, we figure out R2. This is what sets the LED current. You want 700 mA. D1 drops 1.4 V, and let's say the transistor saturates to 300 mV. That leaves 3.3 V across the resistor. (3.3 V)/(700 mA) = 4.7 Ω. Note that this resistor will dissipate (3.3 V)(700 mA) = 2.3 W.
Now for the base resistor. You need 700 mA collector current, so you need at least that divided by the transistor gain as base current. Let's say the minimum guaranteed gain of the transistor at 700 mA is 50. (700 mA)/50 = 14 mA minimum required base current. Figure the B-E drop will be 750 mV, so that leaves 4.25 V across R1. (4.25 V)/(14 mA) = 304 Ω. So the largest common value that guarantees everything within spec is 270 Ω.
Thanks to @Zulu in the comments above for suggesting MOSFETs as an alternative. That turns out to have been the magic bullet. Because the gates don't sink any current, the gate bias can be zero, which makes it much faster.
However, for the secondary side, the board lacks any emitter-to-base (actually now source to gate) bias resistor, so those boards can't take a MOSFET for the secondary. However, on the secondary side, I can use a BJT array with a lower base resistor to speed that up too. I was unable to use a lower base bias on the primary side because then the pull-up had to be too low.
This hybrid approach yields rise and fall times of almost exactly 1 µs on the prototype on the bench, which is just fine (plenty of margin for component variance).
I'm ordering new boards, however, that will have the footprint for the source-to-gate bias resistor. Testing a four MOSFET design with discrete components yielded rise and fall times of closer to 500 ns.
Of particular note is that the SOT-23 and TSSOP-6 footprints for these components turned out to be compatible - swapping out a P-channel MOSFET for a PNP BJT doesn't require any pin movements. Yay!
Best Answer
You should just plug this circuit topology into circuit simulator and start experimenting to figure out on your own how these work. This way you will learn the most.
These circuits use one transistor as a constant current circuit (sinking in your left circuit / sourcing in the right circuit) to linearly discharge / charge the capacitor. The other transistor is driven by the square wave to quickly charge / discharge the capacitor on one state of the square wave signal.
To convince you that the circuits work I plugged the right side circuit with the current source into the LTSpice with some nominal values and obtained the following results.