Лестничные резисторные цепи и цифро-аналоговое преобразование.

Electrical circuit
A resistor ladder is an electrical circuit made from repeating units of resistors, in specific configurations. An R–2R ladder configuration is a simple and inexpensive way to perform digital to analog conversion (DAC), using repetitive arrangements of precise resistor networks in a ladder like configuration.

A 1953 paper "Coding by Feedback Methods" describes "decoding networks" that convert numbers (in any base) represented by voltage sources or current sources connected to resistor networks in a "shunt resistor decoding network" (which in base 2 corresponds to the binary weighted configuration) or in a "ladder resistor decoding network" (which in base 2 corresponds to R–2R configuration) into a single voltage output. The paper gives an advantage of R–2R that impedances seen by the sources are more equal. Another historic description is in US Patent 3108266, filed in 1955, "Signal Conversion Apparatus".

A string of many resistors connected between two reference voltages is called a "resistor string". The resistors act as voltage dividers between the referenced voltages. A Kelvin divider or string DAC is a string of equal valued resistors.

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). The main disadvantage is that this architecture requires comparators, one for each resistor; and this number cannot be reduced by using an R 2R network because such a network would not have separate outputs for each voltage.

A resistor string can function as a DAC by having the bits of the binary number control electronic switches connected to each tap.

The binary weighted configuration uses power of two multiples of a base resistor value. However, as the ratios of resistor values increases, the ability to trim the resistors to accurate ratio tolerances becomes diminished. More accurate ratios can be obtained by using similar values, as is used in R–2R ladder. Hence R–2R provides more accurate digital to analog conversion.

Since the output impedance is independent of digital code, the analog output may equally well be taken as a current into a virtual ground, a configuration called current mode (or sometimes inverted mode). Using current mode, the gain of the DAC may be adjusted with a series resistor at the reference voltage terminal. The current for all bits pass through an equivalent resistance of 2R to ground. The less significant the bit, the more resistors its signal must pass through. At each node each bit's current is divided by two.

Resistors used with the more significant bits must be proportionally more accurate than those used with the less significant bits; for example, in the R–2R network discussed above, inaccuracies in the bit 4 (MSB) resistors must be insignificant compared to  (~3.1%) of R. Further, to avoid problems at the 100002 to 011112 transition, the sum of the inaccuracies in the lower bits must also be significantly less than that. The required accuracy doubles with each additional bit: for 8 bits, the accuracy required will be better than (~0.4%). However, variances for resistances when manufactured in a single component tend to be much lower than variances between components or between batches of manufacturing, and hence a resistor network can be purchased as a single component. And within integrated circuits, high accuracy R–2R networks may be printed directly onto a single substrate using thin film technology, ensuring the resistors share similar electrical characteristics. Even so, they must often be laser trimmed to achieve the required precision. Such on chip resistor ladders for digital to analog converters achieving 16 bit accuracy have been demonstrated.

It is not necessary that each "rung" of the R–2R ladder use the same resistor values. It is only necessary that the "2R" value matches the sum of the "R" value plus the Thévenin equivalent resistance of the lower significance rungs. Figure 2 shows a linear 4 bit DAC with unequal resistors. This allows a reasonably accurate DAC to be created from a heterogeneous collection of resistors by forming the DAC one bit at a time. At each stage, resistors for the "rung" and "leg" are chosen so that the rung value matches the leg value plus the equivalent resistance of the previous rungs. The rung and leg resistors can be formed by pairing other resistors in series or parallel in order to increase the number of available combinations. This process can be automated.