R2R network
The R2R network is an electronic circuit made up of resistors and one of several circuit technologies to convert digital values into an analog voltage, see ( Digital-to-analog conversion ). R / 2R resistor networks are used both in chips and for inexpensive replacement of the same.
construction
An R / 2R network is made up of resistors with the two values R and 2R. The individual input bits, shown here schematically as switches, are either on ground or on the reference voltage depending on the circuit state and feed in via resistors (2R) that are twice as large as the horizontal part (R) of the network. Each bit thus contributes its specific part to the resulting output voltage.
In many applications, R2R converters require a downstream operational amplifier to provide the required power at the output .
Commercial digital-to-analog converter ICs, so-called flash converters, have integrated such R / 2R networks with amplifiers.
properties
advantages
- very high speed
- easy to understand
- consists of similar components
- (theoretically) expandable to any accuracy without loss of speed
- Usually the cheapest solution for low resolutions
disadvantage
- the resistance values must be as equal as possible, especially those for the more significant bits. Since this cannot be achieved in practice even through component selection, the maximum resolution remains limited
- many components are required (this is why R2R networks are sometimes referred to as "resistance graves")
- the more significant bits must drive a large proportion of the output load when switching; therefore often between each input bit and the associated resistors operational amplifier connected
- Compensation of inaccuracies through software calibration is hardly possible
- Brief false voltages arise when switching
Explanation
In the following, the load resistance R L = 2R is assumed and it is assumed that only one changeover switch is on + U ref and all others are on ground. As you can see, the total resistance to the right and left of the node is 2R (highlighted in yellow), so that the current I flowing to the node via S1 is divided into the two partial currents 0.5 I. The current 0.5 I thus flows to the next node further to the right, which is again divided into the two partial currents 0.25 I. This continues with each additional node. The switch S1 thus causes the current 0.125 I via R L , S2 effects 0.25 I (if it is on + U ref ) and S3 causes 0.5 I. If, contrary to the assumption, several switches are simultaneously on + U ref , superimpose the currents originating from the individual switches. Seen from the switches, the network has the resistance 3R, so the current flowing through the switch is I = U ref / 3R. The current flowing through R L and the output voltage U a can thus be calculated.
Equivalent circuit diagram
Viewed from the load resistance R L , the network is a voltage source with the internal resistance R. The switch position is irrelevant because the internal resistance of the voltage source U ref is by definition zero and the voltage source is therefore to be regarded as a short circuit. R L can have any values. The output voltage changes, but the gradation remains correct. U n is the open circuit voltage when no load resistor is connected (R L = ∞).