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When a basic digital to analog conversion is required a resistor ladder is the perfect choice. In this post we discuss how to build a resistor ladder, application limitations and how application specific resistor networks can mitigate the impact of those limitations.

Resistor Ladder Circuit Operation

Individual bits of a digital word are input to the ladder circuit, as shown in the resistor network diagram below, switched between a reference voltage (high – 1) and ground (low – 0). If all inputs (bits) are switched low the output voltage is zero, if all inputs are switched high the output voltage approaches the reference voltage and if inputs are a combination of high and low then the output voltage will be between zero and the reference voltage.

Where inputs vary between high and low the most significant bit (MSB) has the most impact on the output voltage while (as the name suggests) the least significant bit has the lowest impact. Hence, with bit1 as the MSB if only bit 1 is high the output voltage equals Vreference/2. If only bit 2 is high the output voltage equals Vreference/4 and if only bit 8 is high the output voltage equals Vreference/256. Depending on which bits are high or low a proportionate voltage is delivered at the output. The number of inputs (bits) therefore determines the resolution at the output.

Application Issues

As the ladder operates as an array of voltage dividers, resistors within the ladder should be matched (as close as practical) so that the voltage ratio for a given bit is precisely half that of the preceding bit. From the above discussion it should be noted that the impact on the output voltage of changing the least significant bits is small. The potential impact on output voltage accuracy as a result of variations in resistor tolerance across the array should therefore be obvious. Variations in the temperature coefficient of resistance (TCR) and drift in resistance over the resistor life across the array will also impact on output accuracy.

As noted above a voltage switched between the reference voltage and ground acts as a digital input to the resistor ladder circuit. The switches often have some nominal resistance which is effectively in series with the 2R resistor impacting on the value of the 2R leg of the circuit and the accuracy of the voltage output.

The Advantages Of Resistor Networks

Resistor networks designed and manufactured by specialist thick film resistor manufacturers can resolve typical resistor ladder application issues and deliver a device capable of producing an accurate output regardless of the application environment.

Thick film resistor networks are mechanically robust and can be constructed as vertical in line devices to maximise thermal performance. Resistors can be closely matched to eliminate tolerance issues. As resistor devices may be placed in close proximity on the same substrate the impact of temperature and variations in resistor life may be minimised.

By working closely with the circuit designer a specialist network resistor manufacturer can employ appropriate resistor trimming (2R) during the manufacturing process to eliminate errors caused by switch resistance.