CONCEPTUAL TOOLS By: Neil E. Cotter OUTREACH PROJECT CIRCUITS Voltage-Controlled Oscillator. Fig. 1. Voltage-controlled Oscillator.

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1 Voltage-Controlled Oscillat CIRCUIT: The circuit shown below in Fig. 1 produces a rectangular wave with frequency controlled by potentiometer,, R b. The duty cycle varies with v ctrl. F an op-amp such as the LM324 with asymmetric rail voltages, the duty cycle will be greater than 50% when the control voltage is at reference. A control voltage halfway between the rail voltages, however, does produce a 50% duty cycle wavefm. Fig. 1. Voltage-controlled Oscillat. The first part of the circuit produces a voltage reference, v ctrl, that acts as v i plus a diode v-drop, (of approximately 0.65V), when v o is positive and as v i minus a diode v-drop when v o is negative. Fig. 2 shows the wavefms f the oscillat with nonzero input voltage, v i = 0.85V. Fig. 2. Oscillat wavefms f LM324 op-amp [1] with ±5V supplies, = R b, and v i = 0.85V.

2 V-Controlled Oscillat (cont.) Fig. 3 shows the wavefms f the oscillat with input voltage v i = 0V. Fig. 3. Oscillat wavefms f LM324 op-amp [1] with ±5V supplies, = R b, and v i = 0V, [1]. When the output goes high, the capacit starts charging toward the positive rail voltage. The positive rail voltage, along with potentiometer,, R b, and the control voltage, v ctrl, create a voltage divider that determines how high the output voltage, v o, rises befe the op-amp, acting as a comparat, switches to negative rail voltage output. The same voltage divider is now fed by a negative voltage that determines how low the output voltage, v o, drops befe the op-amp, acting as a comparat, switches to positive rail voltage output. The cycle then repeats. Analysis of circuit: To determine the timing of the output wavefm, we solve RC charging problems f the rising capacit voltage. The solution f falling capacit voltage is obtained by switching the v +rail and v -rail and inverting the value of v ctrl. The initial voltage f the RC charging problems is the trip point, v p in Fig. 2, determined by the voltage divider fed by v o and v ctrl. v C (0 ) = v p (0 ) = v -rail R b + v ctrl + R b The final destination voltage is the positive rail voltage f v o, although switching occurs befe this voltage is reached. v C (t ) = v +rail

3 V-Controlled Oscillat (cont.) The time constant, RC, primarily determines the oscillation frequency, whereas v ctrl primarily controls the duty cycle. τ = RC It is recommended that the duty cycle be set first with v ctrl. Then R may be adjusted to set the oscillation frequency. The equation f the charging and discharging curves: v C (t) = v C (0 ) v C (t ) e t/τ + v C (t ). Solving f the time of a half-cycle: v C (t) = v p = v +rail R b + v ctrl = v + R C (0 ) v C (t ) b e t/τ + v C (t ) v C (t) = v +rail R b + v ctrl R a = v rail R b + v ctrl e t/τ + v +rail ln v +rail R b + v ctrl v rail R b + v ctrl = t / τ t = τln v +rail R b + v ctrl v rail R b + v ctrl = τln v rail R b + v ctrl v +rail R b + v ctrl t = τln v rail R b + v ctrl ( ) v +rail R b + v ctrl ( )

4 V-Controlled Oscillat (cont.) t = τln R v b rail + v R ctrl (1+ R b ) a v ctrl = τln, reversing signs in the numerat and denominat, t = τln v +rail v ctrl + (v +rail v rail ) R b v +rail v ctrl F = R b, as in Figs. 2 and 3, v +rail v rail v +rail v ctrl. v ctrl (1+ R b ) + v rail R b v ctrl = τln 1+ v +rail v rail R b v +rail v ctrl R a. F the wavefms in Figs. 2 and 3, we have the following difference of rail voltages: v +rail v rail = 3 ( 5)V = 8V. F the wavefms in Fig. 2, we have the following calculation: 8V V = τln τ 1.85 f output high, and 8V V = τln τ 1.2 f output low. F the wavefms in Fig. 3, we have the following calculations: 8V V = τln τ 1.5 f output high, and 8V V = τln τ 1.05 f output low. Note that the change in timing is on the der of 20%, which is modest, f the examples given.

5 V-Controlled Oscillat (cont.) NOTE: The v i control block could be modified to add an offset to the output voltages in der to produce a square wave. REF: [1] (accessed 23 July 2017)