2.2 Digital-to-Analogue Converters

2.2 Digital-to-Analogue Converters

Digital computers command many analogue actuators and indicators. A display computer may set backlight brightness with a voltage. A flight-control or autopilot computer may send an analogue rate or position command to a servo amplifier that still expects a smooth voltage. Some standby or repeater instruments remain analogue even though the source parameter now lives in a digital air-data or inertial box. The current topic 5.3 heading and levels are broad. The pre-12 June 2024 detailed description identified digital-to-analogue converter (DAC) operation, inputs, outputs, applications, and limitations; this guide retains that useful scope. Category B2 knowledge is level 2; Category B1 is level 1.

A DAC accepts an $n$-bit digital word and a stable analogue reference. It produces a voltage or a current that, in the ideal case, is

$V_{\text{out}} = V_{\text{ref}} \times \frac{D}{2^n}$

for a unipolar straight-binary code $D$ running from $0$ to $2^n-1$. (Some avionics DACs use bipolar offset-binary or two’s-complement coding so that mid-scale is zero volts; the arithmetic changes but the hardware ideas do not.) The analogue resolution is again one LSB, $V_{\text{ref}}/2^n$ (unipolar). The digital input is the only “sensor” the DAC has: garbage codes, stuck bits, or a collapsed reference produce a wrong analogue command even when the processor logic looks healthy on a bus analyser.

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Binary-Weighted Resistor DACs

The classical weighted-resistor (or binary-weighted) DAC uses a resistor for each bit whose conductance is proportional to that bit’s binary weight. For a 4-bit example the resistors are $R$, $2R$, $4R$, and $8R$ (or the current-defining set $R/8$, $R/4$, $R/2$, $R$). Each bit switch connects its resistor either to the reference or to analogue ground. The weighted currents (or voltages) are summed, usually at the inverting node of an operational amplifier.

The architecture is easy to draw and easy to explain in an oral board, which is why it still appears in basic-knowledge teaching. It is much harder to manufacture at 12 bits and beyond. An 8-bit weighted network already needs a resistance ratio of $128:1$ between the most-significant and least-significant bit. Those resistors must track over the full airborne temperature range, or the bit weights cease to be binary. A single out-of-tolerance most-significant-bit resistor can create a large differential non-linearity (DNL) error — a jump that is much larger or much smaller than one LSB — and can destroy monotonicity.

Switch on-resistance adds another error. The most-significant-bit switch carries the largest current, so a few ohms of MOSFET resistance steal a significant fraction of that bit’s weight unless the design uses force-sense switching or very large devices. For these reasons, discrete weighted-resistor DACs are rare in modern line-replaceable units except in low-resolution, non-critical analogue trims.

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R-2R Ladder DACs

The R-2R ladder uses only two resistance values, $R$ and $2R$, arranged so that each bit node sees the same equivalent resistance looking downstream. A bit switch steers the node current either to the summing amplifier or to ground (current-mode ladder) or switches the node between $V_{\text{ref}}$ and ground (voltage-mode ladder). Because every rung is $R$ or $2R$, integrated-circuit processes can match the ratio tightly. A 12-bit monolithic DAC is therefore almost always an R-2R ladder or a segmented variant of the same idea, not a 12-resistor binary-weighted string stretching from $R$ to $2048R$.

Current-mode ladders are fast: the switch nodes sit at a virtual earth and the parasitic capacitances do not have to slew through large voltages. Voltage-mode ladders can be simpler when a buffered voltage output is required and speed is modest. In either case the reference must be quieter and more stable than one LSB if the analogue command is to remain inside its error budget. Reference drift with temperature appears as a gain error that scales every code, including full-scale brightness or full-scale servo demand.

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Current Output versus Voltage Output

Many DAC integrated circuits are current-output devices. The ladder (or a set of weighted current sources) delivers $I_{\text{out}}$ into a virtual-earth summing node. An external or on-chip transimpedance amplifier converts that current to a voltage, $V_{\text{out}} = -I_{\text{out}} R_F$. The feedback resistor and the amplifier’s settling behaviour then become part of the converter’s analogue specification. A technician probing the DAC pin may see a current, not a voltage; the “DAC output” the servo actually uses is after the amplifier.

Voltage-output DACs include the buffer. They are convenient for driving high-impedance loads such as display dimming inputs or analogue meter movements through a further isolation stage. They are less convenient for driving low-impedance loads or long screened cables: the buffer must supply current, reject the cable capacitance, and still settle inside the LSB band. In either style the DAC does not create energy from the digital word. The analogue power comes from the reference and the supply rails. A collapsing $5\text{ V}$ analogue rail will pull every brightness and servo command toward the wrong end-stop even if the digital data bus remains perfect.

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Settling Time, Glitches and Monotonicity

Settling time is the interval from a digital code change until the analogue output enters and remains inside a specified error band, commonly $\pm \tfrac{1}{2}\text{ LSB}$ (sometimes $\pm 1\text{ LSB}$ on slower parts). Major-carry transitions — for example $01111111$ to $10000000$ — are the worst case, because every bit switch changes at once. During that instant the output can show a narrow glitch: a spike caused by unequal switch timing. A following analogue filter or a deglitching sample-and-hold is often used when the DAC drives a servo that would otherwise twitch.

Monotonicity means that if the digital input increases by one LSB, the analogue output does not decrease. A monotonic 12-bit DAC may still have DNL errors smaller than one LSB; it will never reverse direction on a rising ramp of codes. A non-monotonic DAC can make a closed-loop servo hunt or an analogue pointer jump backward as the computed parameter increases. Integral non-linearity (INL) describes the bow of the transfer curve relative to the ideal end-point or best-fit line; large INL is an accuracy problem even when the converter remains monotonic.

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Offset Error, Gain Error and Other Limitations

Offset error is the analogue output when the digital input is the zero code (or the bipolar mid-scale code). It shifts every point on the transfer curve by the same voltage. Gain error is the error in the slope: full-scale output is not exactly $V_{\text{ref}}\times(2^n-1)/2^n$. In service, offset often tracks input-amplifier or buffer drift; gain often tracks the reference. Neither error is cured by “more bits” if the analogue reference has moved.

Other practical limitations that Module 05 expects you to name:

• Resolution versus accuracy, exactly as in Section 2.1: a 16-bit DAC can still be inaccurate.
• Temperature coefficients of the reference, the ladder, and the output amplifier.
• Supply rejection: ripple on analogue rails appears on $V_{\text{out}}$.
• Digital feedthrough and clock noise on the analogue pin.
• Load regulation and the inability of a voltage DAC to drive a heavy analogue meter without a buffer.
• Code-dependent output impedance on unbuffered current-output pins.

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Aircraft Applications

Display brightness and flooding. Electronic flight instrument and crew-alerting displays need analogue lamp or backlight drive that follows a digital dimming word from the display computer or a lighting-control panel. The DAC output is usually a voltage or a low-frequency pulse-width command reconstructed to analogue. Settling time matters when the crew selects a new lighting preset; a slow or ringing DAC is seen as flicker. Offset error appears as a residual glow at the “off” code; gain error appears as a display that will not reach full day brightness.

Servo and actuator commands. Many autopilot, yaw-damper, and engine-control interfaces still present an analogue voltage or current to a servo amplifier even though the control law is digital. The DAC is then inside the command path. Non-monotonicity or large glitches can be interpreted as a command reversal. Conversion must settle inside the servo’s inner-loop sample time. Technicians tracing a “digital box, analogue jack” interface should measure the analogue command with the digital word known from BITE, not assume the pin voltage is a raw sensor.

Analogue cockpit instruments driven from digital boxes. Repeater altimeters, analogue standby interfaces, and older engine gauges may be driven from a digital air-data or engine computer through a DAC (or through a synchro/resolver wrapper that itself contains conversion). The limitation set is the same: reference integrity, monotonicity, settling, and the analogue cable. A digital parameter that is correct on the bus can still drive a wrong analogue pointer if the DAC reference or the instrument buffer has failed.

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Worked Numerical Example: 8-bit Brightness DAC

A unipolar voltage-output DAC sets display backlight command from $0\text{ V}$ to a $5.000\text{ V}$ reference. The digital word is 8 bits.

Step 1 — Resolution

$V_{\text{LSB}} = \frac{5.000\text{ V}}{256} = 19.53\text{ mV}$

Step 2 — Ideal output for code $D = 200$

$V_{\text{out}} = 5.000\text{ V} \times \frac{200}{256} = 3.906\text{ V}$

Step 3 — Offset and gain

If the measured output at code $0$ is $+15\text{ mV}$, the offset error is $+15\text{ mV}$ (less than one LSB). If the measured full-scale code $255$ is $4.900\text{ V}$ instead of $5.000\times 255/256 = 4.980\text{ V}$, there is a gain error of about $-80\text{ mV}$ at the top of the scale. The display will never reach the intended day brightness until the reference or the gain path is corrected.

Step 4 — Settling

If the servo or lighting amplifier requires the analogue voltage to be inside $\pm \tfrac{1}{2}\text{ LSB}$ ($\pm 9.8\text{ mV}$) within $20\text{ }\mu\text{s}$, a DAC whose datasheet settling time is $50\text{ }\mu\text{s}$ is the wrong part, regardless of its 8-bit resolution.

[!NOTE] Inputs, outputs, and limitations belong in the same breath. The input is the digital word plus the analogue reference and supplies. The output is a voltage or a current that must be buffered for the real load. The limitations — settling, monotonicity, offset, gain, glitch, temperature, and load — decide whether that pin is fit to drive a brightness input, a servo, or an analogue instrument.