Page 379 - Op Amps Design, Applications, and Troubleshooting

Dual-Slope A/D Conversion 355

an
The current through K 2 c be found with Ohm's Law, since it has 1 volt on the left
end and 2 volts on the right end.

Again, Kirchhoff's Current Law will let us conclude that if 2 milliamperes
are flowing to the left through RI and 0.5 milliampere is flowing to the right
through JR 2/ then capacitor C must still be charging with a 2.5-milliampere current.
Let us examine the circuit at one more point.
Suppose we let capacitor C accumulate a charge of 4 volts. The current
through RI will then be

With +4 volts on the capacitor, the output voltage of the op amp must be

can
The current through R 2 be calculated as

Finally, we apply Kirchhoff's Current Law to show that with 0.5 milliampere
flowing right to left through RI and 2 milliamperes flowing left to right through
R2, there must surely be 2.5 milliamperes flowing upward through capacitor C.
Since the current through capacitor C has remained constant at 2.5 milBamperes,
we know that the voltage across it will be a linearly rising ramp. The slope of the
ramp is given by the basic capacitor charge equation:

For the present case, the slope of the ramp across C is computed as

The output of the op amp will have a slope that is linear but twice as great, since the
amplifier has a voltage gain of 2. In either case, the slope of the ramp is determined
by the charging current of C, which is determined by the value of input voltage.