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In the study of electronics, the concept of duty-cycle pops up in various places such as digital circuits, one-shots, switching regulators, and DA converters to mention a few. Lab experiments to examine duty-cycle usually require two parts- a square-wave oscillator driving a monostable multivibrator (one shot).
A common circuit involves two 555 chips and a bunch of resistors and capacitors for each chip. Also, the RC time constant associated with the capacitor coupling the two 555s is critical.

In contrast, the circuit shown in Figure 1 can be built with a single IC, two capacitors, three resistors, two trim-pots, and a diode. The component values and time-constants are not critical. And with this simple circuit, here is what you can demonstrate:

What is hysteresis

What is a Schmitt-trigger input

How can hysteresis be used to build a square-wave oscillator

What is duty cycle

How do you adjust duty-cycle to different values

How does duty-cycle relate to DC value

What is a low-pass filter

How does filter cut-off relate to square-wave frequency

How does filter time-constant relate to speed of response to changing duty-cycle

Of course, with such a simple circuit you would expect that there was some kind of trade-off. And you’re right: this circuit changes frequency as you change duty-cycle. But even with that limitation, you can still demonstrate all the items listed above. And you can use this circuit as a lead-in to a follow-up experiment with a circuit that maintains constant frequency as you vary duty-cycle.

The key to the circuit is the CD4093 CMOS digital IC. It’s a quad two-input NAND gate chip with Schmitt-trigger inputs. In an inverting configuration, driving the inputs high will force the output low, while driving the inputs low will force the output high. The value of the input voltage that causes the output to change is the switching-threshold. The switching-threshold on a Schmitt-trigger input is not fixed; it has one of two different values depending on whether the output is high or low. In the 4093, the input voltage to force the output low is higher than the input voltage that forces the output high. The result is a hysteresis effect.

We all have experience with the property of hysteresis. It can be seen in an old-fashion oil-can, the kind with a long flexible spout on a semi-spherical can with a wide, flat bottom. You pick the can up with one hand: the spout between your fingers and your thumb on the bottom. As you press on the bottom of the can, nothing happens until there is enough pressure to “pop” the bottom in and a squirt of oil comes out. As you release the pressure, the bottom will “pop” back out at less pressure than it took to “pop” it in.

The way hysteresis leads to oscillation can be seen in an automobile with a loose “front end”. As you turn the steering wheel, nothing happens at first. Then, at a certain point, the car will turn. As you turn the wheel back to “straighten out”, again nothing happens until you get to a point where the car suddenly swerves the other way. The result is that, as you travel down the road, the car is swerving left and right. You can’t get it to go in a straight line. In effect, you’re oscillating.

In this circuit, let’s assume that C1 is discharged, making the input of the IC low and causing its output to go high. The voltage on the high output is fed back to the input through R1, R2, D1 and R3. The resistors limit the current, so C1 charges up with a certain time-constant. When the Voltage on C1 reaches a certain point, call it V1, it will be high enough to force the output low. At that point C1 will start to discharge through R3 only, since D1 will be reverse-biased. When the Voltage on C1 drops to a certain point, call it V2, it will be low enough to force the output high again. The cycle then repeats, and we have made a square-wave oscillator. Note that it is necessary that V1 be a higher value than V2 so that there is a fixed amount of Voltage that C1 must charge and discharge to produce a cycle. Then by changing the resistance, the time needed to charge and discharge (and thereby the frequency) can be changed.

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