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Connecting passive components to logic gates

Posted: 14 May 2015 ?? ?Print Version ?Bookmark and Share

Keywords:Digital gates? transistors? CMOS? PWM? voltage-controlled oscillator?

Digital gates are fundamentally analogue in nature. They use transistors. Sure, these transistors are operated at their conduction extremes (which is why they are called "digital"), but during the logic state transition they're pure analogue. By adding a few passive components, you can make circuits such as level converters, frequency multipliers, phase detectors, line drivers, and pulse changers.

Take the simplest form of a passive component attached to a gate. A pull-up/pull-down resistor sets the logic level to an unused digital input (an absolute must with discrete CMOS). Open drain/collector/emitter outputs also require a pull-up/pull-down resistor to set the digital levels using analogue means.

But it gets more interesting when we look at how we can use gates along with passives as timing or averaging elements. The most basic duty-cycle to analogue-level conversion is accomplished with a simple RC filter in figure 1.

Figure 1: Adding an RC filter to a logic gate produces a level voltage output with ripple.

Pulse-width-modulation (PWM) derives an analogue DC voltage level that results from the timing ratio between the successive high and low logic levels applied to the RC filter network. Starting from 0V on the capacitor, each successive high pumps the capacitor a little higher in voltage until an equilibrium is reached after about five RC time constants. There will always be a small ripple on the averaged DC level (exaggerated in the figure). For best results, make the pulse frequency as high as possible, and make the RC time constant as long as possibleconsistent with the required settling time.

We can take advantage of this effect in the most basic of digital-type phase detectors (figure 2). The exclusive-OR function can be used in phase-locked-loops because the RC-filtered output voltage is directly proportional to the duty cycle resulting from the phase difference between its two input signals.

Figure 2: An XOR gate, voltage-controlled oscillator, and a few passive components make a frequency doubler.

Feeding this RC filtered DC level back to the VCO servos its frequency into lock with the reference frequency. The resulting phase difference between the VCO output and the reference depends on the voltage that the VCO requires to run at the same frequency as the reference.

A side-effect is the frequency doubling aspect of the XOR phase detector. In fact, a similar effect can be harnessed as a frequency multiplier (figure 3).

Figure 3: Make a frequency multiplier with a XOR gate, an op amp, two capacitors, an inductor, and a delay.

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