Resistor ladder
A resistor ladder is an electrical circuit made from repeating units of resistors. Two configurations are discussed below, a string resistor ladder and an R–2R ladder.
An R–2R Ladder is a simple and inexpensive way to perform digital-to-analog conversion, using repetitive arrangements of precise resistor networks in a ladder-like configuration. A string resistor ladder implements the non-repetitive reference network.
A string of many, often equally dimensioned, resistors connected between two reference voltages is a resistor string ladder network. The resistors act as voltage dividers between the referenced voltages. Each tap of the string generates a different voltage, which can be compared with another voltage: this is the basic principle of a flash ADC (analog-to-digital converter). Often a voltage is converted to a current, enabling the possibility to use an R–2R ladder network.
A basic R–2R resistor ladder network is shown in Figure 1. Bit an−1 (most significant bit, MSB) through bit a0 (least significant bit, LSB) are driven from digital logic gates. Ideally, the bit inputs are switched between V = 0 (logic 0) and V = Vref (logic 1). The R–2R network causes these digital bits to be weighted in their contribution to the output voltage Vout. Depending on which bits are set to 1 and which to 0, the output voltage (Vout) will have a corresponding stepped value between 0 and Vref minus the value of the minimal step, corresponding to bit 0. The actual value of Vref (and the voltage of logic 0) will depend on the type of technology used to generate the digital signals.
For a digital value VAL, of a R–2R DAC with N bits and 0 V/Vref logic levels, the output voltage Vout is:
For example, if N = 5 (hence 2N = 32) and Vref = 3.3 V (typical CMOS logic 1 voltage), then Vout will vary between 0 volts (VAL = 0 = 000002) and the maximum (VAL = 31 = 111112):
with steps (corresponding to VAL = 1 = 000012)
The R–2R ladder is inexpensive and relatively easy to manufacture, since only two resistor values are required (or even one, if R is made by placing a pair of 2R in parallel, or if 2R is made by placing a pair of R in series). It is fast and has fixed output impedance R. The R–2R ladder operates as a string of current dividers, whose output accuracy is solely dependent on how well each resistor is matched to the others. Small inaccuracies in the MSB resistors can entirely overwhelm the contribution of the LSB resistors. This may result in non-monotonic behavior at major crossings, such as from 011112 to 100002. Depending on the type of logic gates used and design of the logic circuits, there may be transitional voltage spikes at such major crossings even with perfect resistor values. These can be filtered with capacitance at the output node (the consequent reduction in bandwidth may be significant in some applications). Finally, the 2R resistance is in series with the digital-output impedance. High-output-impedance gates (e.g., LVDS) may be unsuitable in some cases. For all of the above reasons (and doubtless others), this type of DAC tends to be restricted to a relatively small number of bits; although integrated circuits may push the number of bits to 14 or even more, 8 bits or fewer is more typical.
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