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A resistor ladder is an electrical circuit made of repeating units of resistors. Two configurations are discussed below, a string resistor ladder and a R-2R ladder.
An R-2R Ladder is a simple and inexpensive way to perform digital-to-analog conversion, using repetitive arrangements of precision resistor networks in a ladder-like configuration. A string resistor ladder implements the non-repetitive reference network.
Network or circuit composed of a sequence of L networks connected in tandem. Circuit used in digital to analog converters.
R-2R resistor ladder network (digital to analog conversion, or DAC). A basic R-2R resistor ladder network is shown in Figure 1. Bit4 MSB (most significant bit) to Bit0 LSB (least significant bit) are driven from digital logic gates. Ideally, the bits are switched between 0 volts (digital 0) and Vref (digital 1).
The R-2R network causes the digital bits to be weighted in their contribution to the output voltage Vout. In this circuit 5 bits are shown, giving 32 possible outputs. Depending on which bits are set to 1 and which to 0 the output voltage (out) will be a stepped value between 0 volts and (Vref minus the value of the minimum step, Bit0).
The actual value of Vref (and 0 volts) will depend on the type (technology) of the digital logic gates used to drive Bit4-0.
For a digital value VAL, of a R-2R DAC of N bits of 0 V/Vref, the output voltage Vout is:
Vout = Vref × VAL / 2N
In the example shown, N = 5 and hence 2N = 32. With Vref = 3.3 V (typical CMOS logic 1 voltage), Vout will vary between 00000, VAL = 0 and 11111, VAL = 31.
Minimum (single step) VAL = 1, we have
Vout = 3.3 × 1 / 32 = 0.1 volts
Maximum output (11111 VAL = 31, we have
Vout = 3.3 × 31 / 25 = 3.2 volts
The R-2R ladder is inexpensive and relatively easy to manufacture since only two resistor values are required (or 1, 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 higher significant bit resistors can entirely overwhelm the contribution of the less significant bits.
Digital to Analog Converter with R 2R Ladder Network - Video:
R-2R Ladder Application - Video: