T-Type Resistor Network D/A Converter (DAC)

The circuit illustrated is an 8-bit T-type resistor network D/A converter (DAC), whose core function is to convert digital signals into analog voltages through a resistor network. Below is a detailed analysis of the circuit logic:

1. Circuit Structure and Component Functions

1.1 Resistor Network:

1. Utilizes an R-2R type resistor network, consisting of only two types of resistors (R and 2R), simplifying circuit design and improving accuracy.
2. The input branch (horizontal) resistors are R, and the branch resistors at each node (vertical) are 2R, forming a chain structure.

1.2 Switch Array:

1. Each digital input bit (D7~D0) controls a double-pole double-throw switch:
1. When Di=1, the switch connects to the inverting input of the operational amplifier (virtual ground, potential ≈0);
2. When Di=0, the switch connects to ground (potential=0).

1.3 Operational Amplifier and Feedback Resistor (Rfb):

1. The operational amplifier operates in inverting amplification mode, converting the current output from the resistor network into a voltage;
2. Rfb is the feedback resistor, determining the gain of the current-to-voltage conversion.

2. Current Distribution and Binary Weighting

2.1 Total Input Current Calculation:

1. The total current I flowing from the reference voltage VREF is calculated as I=VREF/R_total, where R_total=R+2R=3R (since the equivalent resistance at each node is 2R, the total resistance of the chain structure is 3R), thus I=VREF/3R.

2.2 Current Splitting Rule:

1. Each node splits the current evenly: after passing through the first R, the current I splits into two paths 1/2 (one path flows into 2R to ground, the other continues to the next level);
2. Each level of current is halved according to binary weighting: D7 corresponds to the highest bit, current is 1/2; D6 is 1/4, and so on, D0 corresponds to the lowest bit, current is 1/256 (the total weight for 8 bits is 2^8=256).

2.3 Effective Output Current:

1. When Di=1, the current through the corresponding branch’s 2R resistor flows to the operational amplifier’s virtual ground, forming the output current Iout;
2. When Di=0, the current directly connects to ground and does not contribute to the output.
3. The total output current is the sum of the currents from all effective bits: out=I/2^D7+I/4^D6+⋯+1/256^D0=1/256∑_i=0⁷Di⋅2^7-i

3. Output Voltage Derivation

3.1 Virtual Short Circuit Characteristic of Operational Amplifier:

1. The potential at the inverting input is 0 (virtual ground), the output voltage VO=−Iout⋅Rfb (the negative sign is due to the inverting input).

3.2 Substituting the Current Expression:

1. I=VREF/3R, the total output voltage is: VO=−Rfb⋅3R⋅VREF/256∑_i=0⁷Di⋅2^7-i
2. If we take Rfb=3R (a common design), it simplifies to: V0=−VREF/256⋅N (where N=D7D6⋯D0 in decimal value, 0≤N≤255) VO=−256VREF⋅N (where N=D7D6⋯D0 in decimal value, 0≤N≤255)

4. Key Features Summary

1. Resolution: 8 bits, capable of outputting 2^8=256 voltage levels.
2. Linearity: Depends on resistor accuracy, the R-2R network inherently possesses good linear characteristics.
3. Output Range: When N=0, VO=0; when N=255, VO=−255/256VREF (close to but not reaching −VREF).
4. Advantages: Fewer types of resistors, easy to integrate, low power consumption, widely used in early DAC designs.

5. Example Calculation

Assuming VREF=5V, Rfb=3R, and the input digital code is 10000000 (D7=1, others are 0):

• N=128,
• VO=−5/256×128=−2.5V, which meets the expectation that the highest bit weight is VREF/2.

This circuit achieves a linear mapping from digital signals to analog voltages through binary weighted current distribution and operational amplifier conversion, making it one of the classic architectures of DACs. Personal summary: The conversion from digital signals to analog voltage output is achieved through binary weighting, controlling the output voltage according to design requirements.