Digital-to-analog (d/a) converters

The conversion current that implements the digital signal to the analog signal is called a digital-analog (d/a) converter, referred to as the DAC (Digital-analog convert).

At present, the common d/a converters are: Power resistor network D/A converter, inverted t resistor network D/A converter, weight current type D/a converter, weight capacitance network D/A converter, switch tree D/A converter

First, the expression of digital signal

In digital signals, we use binary to express the size of the digital signal, such as an n-bit binary with dn=dn-1*dn-2*......d1d0, wherein a multi-bit binary number of each bit of 1 represents the value of the size of this bit of the right, The weights from Highest bit (MSB) to lowest bit (LSB) are 2^n-1, 2^n-2 、......、 2^1, 2^0

Second, the right resistor network D/A converter

　　

For example, the states of S3, S2, S1, and S0 are controlled by code D3, D2, D1, and D0 respectively, the code is 1 o'clock, the switch is connected to the reference voltage Vref, and the code is grounded on the 0 o'clock switch.

The summation amplifier is a negative feedback op amp, the ideal amplifier has an open-loop magnification of infinity, its input current is 0 (the input resistor is infinite), the output resistance is zero .

When the reference voltage is added to V by the resistor network, as long as the V is slightly higher than v+, the output voltage is very negative in VO, V0 rf feedback to the V-end to reduce V, the result will inevitably make v-≈v+=0

Under conditions where the OP amp input current is zero: v0=-rf*i=-rf* (i3+i2+i1+i0)------------------①

Due to the v-≈0, the branch currents are respectively

By substituting the DC current into the formula ①, and taking the RF=R/2, you can get:

For n-bit weighted resistor network d/A converters, when the feedback resistor is taken as R/2, the output voltage is calculated as

Since then, we can extract the expression form of the digital signal:

That is, when dn=0, Vo=0, when dn=11...11,

The advantages of this circuit is that the structure is relatively simple, the use of a relatively small number of resistive elements, but its resistance resistance of the difference is relatively large, especially in the input signal the number of bits, the problem is more prominent. If the input signal is increased to 8 bits, if the smallest resistor in the network is r=10k, then the maximum resistance value will reach 2^7r=1.28m, which is 128 times times the difference. It is difficult to make sure that each resistor has a high accuracy in a very wide range of resistance, especially for integrated circuits.

To solve this problem, the inverted T-resistor d/A converter can be used.

Three, inverted T-shaped d/a converter

The figure shows that the resistor network has only R, 2R two resistance resistors, which brings great convenience to the design and manufacture of integrated circuits.

For example, from the AA, BB, CC, DD each port to the left to see the equivalent resistance is R, so the reference power inflow to the inverted T resistor network total current of i=vref/r, and each branch of the current is: I/2,I/4,I/8,I/16

If the di=0 switch si ground (that is, the amplifier's v+), and the di=1 switch si amplifier v-, in the summation amplifier feedback resistor value equal to R,

Total Current:

Output voltage (vo=-r*i∑) under the condition of the summation amplifier feedback resistor R:

Similarly, for n-bit input, the inverted T-resistor network D/A converter, in the summation amplifier feedback resistor is r, the output voltage

Digital-to-analog (d/a) converters