Page 202 - Op Amps Design, Applications, and Troubleshooting

Voltage-Controlled Oscillator 185

where I is the input current computed and t is the time Q is allowed to charge,
This equation can be transposed to produce another very useful form:

This allows us to compute the amount of time it takes Q to charge to a given volt-
age change (AV Cl) when a given value of charging current is applied.
We already know from earlier discussions that the limits of Q's charge are
set by the upper and lower thresholds of A^ That is, Q will charge linearly
between the Vjj and V UT values established by A 2. In the present circuit, the
change in C\ voltage in going from the V LT to the V^ is

More specifically,

AV Cl = 46.8 V - (-6.8 V) = 13.6 V

If we now compute the time it takes Cj to make this voltage change, we will know
the time for one alternation (negative slope) of the oscillator's output. Let us com-
pute this time for input voltages of +1 and +5 volts, which were previously shown
to produce 50 microamperes and 250 microamperes, respectively. Equation (4.12)
gives us

The remaining alternation (positive ramp) occurs when D 4 is forward-biased. This
effectively connects the output of A 3 to AI via R 4. Recall that during this portion of
the cycle, the output of A 3 is 0.6 volts larger than + V^ and is of the opposite polar-
ity. Since diode D 4 drops 0.6 volte when it is forward-biased, this means that the
voltage applied to the right end of Rj is exactly the same as the value of +V m, but
it is negative instead of positive. That is, this input to AI ranges from -1 to -5 volts.
The resulting input current through #4 is computed as