Here is a simple oscillator circuit that varies the duty cycle over a wide range without affecting the frequency. It is a variation of the simple 555 astable oscillator. Initially, I told a reader that there was no standard 555 circuit that could do this, but then the grey matter started working. The use of an air-variable capacitor for frequency control is a mind-blower—nothing short of a time warp!

**555 Duty Cycle Control Schematic**

**Overview**

When potentiometer R1 is centered, operation is obvious and the duty cycle is 50%. However, as R1 is rotated in either direction the charge time and discharge times vary accordingly. The two sides of R1 have independent steering diodes (D1 & D2). C1 & C2 make up the timing capacitor. Pins 2 & 6 of the 555 are the upper and lower thresholds of the input comparators. The charge /discharge voltage is taken from pin 3 because it has rail-to-rail voltage swing, and the open collector output (pin 7) cannot do this. The rectangular waveform output is taken from pin 7 instead. R3 is the pull-up resistor.

If constant frequency is desired, C1 could be padded for the correct frequency. However, most experimenters also want variable frequency. Since R1 cannot be varied in total resistance, it cannot vary the frequency. R2 could vary the frequency, but would also affect the duty cycle ratio limits as well. The only practical means of obtaining variable frequency is to vary C1.

**Mathematical proof**

Q = I * T – where Q is the charge, I is charge current and T is charge time

Q = C * V – where Q is charge, C is capacitance, and V is voltage across the capacitor

∴ I * T = C * V

E = I * R – where E is voltage I is current and R is resistance

∴ I * T = C * I * R – because E is simply another expression for V

T = C * R – dividing by I—we have now proved that charge time is directly proportional to R

So we have a charge resistance and a discharge resistance, the sum of which is constant and equal to the R1 potentiometer total resistance (1 to 3). Therefore, the sum of the charge and discharge times is also constant. Since F = 1/T, the frequency is also be constant.

In other words, the two resistances are complementary and the two time periods are likewise complementary.

**The Air Variable Capacitor**

The old-fashioned air variable capacitor is old and klunky. While DigiKey offers no such product, these devices remain available on eBay as used or old stock. Every serious experimenter should have one of these. The one I would buy is a 3-gang 440pf. Wired in parallel the total capacitance is 1320pf. Physical size limitations prevent higher capacitances.

Actually, it is fun to play with air variable capacitors.

**High impedances**

To obtain a reasonably low frequency, R1 had to be selected to have as high a resistance as possible. 2M is the highest value pot I had on hand. A 5M would also be a good selection. To function under such high impedance conditions, I selected the TLC555 CMOS 555. A further advantage of this device is that it has rail-to-rail output voltage—something that the bipolar 555 cannot do.

**Limits of accuracy**

The accuracy tends to degrade when the slew rate at C1 exceeds about 0.25V/uS. When this happens, the propagation delay of the comparators becomes significant and the frequency drops somewhat. This causes the peaks of the saw-tooth waveform to “skid” past the thresholds before the output switches polarity. This forces the maximum frequency to be lower than about 50kHZ for 50% duty cycle, or lower than 2kHZ with 98% duty cycle. To maintain 1 or 2% frequency accuracy the duty cycle range must drop as frequency increases.

**Bench test set-up**

**Oscillographs**

**For the future**

Novel VCO circuit

**Glossary of undocumented words** (for our ESL friends)

Klunky – adjective – variation of clunky – big, cumbersome, ugly, outmoded…

Note that in the mathematical proof, the “delta” symbol should be the “therefore” symbol (3 dots in triangle). ASCII symbols map differently in different language alphabets so I can see how it got mixed up. The word processor I used has the 3 dot symbol available, but when published here ended up as the “delta” symbol.

One detail I missed: The oscillograph of the saw tooth waveform got loaded down by the DC resistance of the scope probe so I isolated the DC component with a capacitor. That is why it is centered at zero volts rather than Vcc/2.

Thank a lot for this circuit.

hi, is there a simple way to provide voltage-controlled pulse-width or frequency in this design? -thx!

Not this simple, nor in this design, but fully doable. The easiest way to get variable frequency is via a voltage controlled oscillator. The easiest way to obtain variable pulse width is to clock a monostable multivibrator via another oscillator and make the monostable timeout a function of a DC voltage