Choosing Component Values for DCO Design

Question

This is a sawtooth DCO, the comparator U1A resets the ramp at the desired frequency (thus controlling the frequency), and the voltage V7 applied to integrator U2A determines the rate of change of the the ramp (determines the amplitude). I am trying to find the values of RS2 and C1 of the integrator circuit.

Known:

1. Maximum Integrator Input Voltage V7 = 5V
2. Desired integrator Output Voltage after 500 microseconds = around 5V
   • (500us since a frequency of 2000Hz as used in equation below)
3. Op amp: TL084

Unknown:

1. RS2
2. C1
3. Input current at maximum voltage

I understand that the current flows straight through (virtual ground), so the equations below should apply. My question is, which value of C1, RS2 or max current is chosen first, and why?

Answer 1

My question is, which value of C1, RS2 or max current is chosen first, and why?

Generally we'll pick the capacitor first. They come in fewer values per decade (E3 or E6 series) than resistors which are available in E12 or E24 series. Pick the capacitor and then calculate the resistor based on that. But the two are intertwined ...

We want to pick a mid-range resistor value. Too low and we'll load the previous stage and need a large capacitor. Too high and we'll suffer bias-current offsets and integration of the bias current. 10k might be a nice value. It would limit the current to 0.5 mA on a 5 V input.

From \$ Q = CV \$ we can differentiate and get \$ I = \frac{dQ}{dt} = C \frac {dV}{dt} \$. Rearranging this we get \$ C = \frac {I}{\frac {dV}{dt}} \$. Using your values of 5 V / 500 µs = 10000 V/s we get \$ C = \frac {0.5m}{10k} = 0.05 \ \text {µF} \$.

Let's increase this to 0.1 µF for convenience and recalculate. \$ I = C \frac {dV}{dt} = 0.1µ \times 10000 = 1 \ \text {mA} \$.

For 1 mA from a 5 V supply we can calculate \$ R_{S2} = \frac {V}{I} = \frac {5}{1m} = 5 \ \mathrm {k\Omega }\$.