Digital to Analog Converters (DAC) 3 ©Paul Godin Created March 2008

R/2R DAC The Binary-Weighted DAC limitations include the need for progressively larger resistors. The R/2R ladder method eliminates the need for the variety of resistors required. It operates on a ratio between resistors. The Op Amp is still an important component in the circuit.

R/2R Circuit VDD VEE Rf R 2R LSB MSB

What value of R does the op-amp input sence? R/2R Circuit VDD VEE Rf R 2R LSB MSB 1 What value of R does the op-amp input sence?

Resistor Equivalent 1 2R R R R 2R 1 2R 2R 2R REQ 2R R

Resistor Equivalent 1 1 REQ 2R R Rf 2R VDD 2R LSB VEE Note: The resistor that connects between the inverting input and ground serves no function. The inverting input of an op amp is already at a “virtual” ground.

R/2R Circuit – Current Perspective VDD VEE Rf R 2R LSB MSB The resistance seen to the right of any vertical resistor is 2R.

Errors in DAC

Errors Digital to Analog systems have several possible sources of error. The errors can be the result of: Binary Input Non-linear input sequences or incorrect values Voltage issues Resistor network Resistors out of specification Noise Op Amp output errors Improper input voltage Improper Offset Delay

Gain Error A Gain Error occurs when the Op Amp produces an output at a different voltage scale than desired. The output is linear but the steps are either larger or smaller than they should be. Output may appear clipped. Red: Ideal Blue: Error Green: Error Volts Binary Code

Gain Error Typical Causes: wrong VDD/VEE at op amp wrong RREF value wrong resistor network values Red: Ideal Blue: Error Green: Error

Offset Error An Offset Error occurs when the Op Amp output has the same voltage per step but the starting voltage is different. Red: Ideal Blue: Error Green: Error Volts Binary Code

Offset Error Typical Causes: op amp improperly offset Red: Ideal Blue: Error Green: Error

Non-Linearity: Non-Monotonic A Monotonic Error occurs when the individual voltage steps are non-linear. Volts Binary Code Red: Ideal Blue: Error

Non-Linearity: Non-Monotonic Typical Causes: incorrect input binary sequence caused by mix-up at binary input or a stuck input Red: Ideal Blue: Error

Non-Linearity: Differential A Differential Error occurs when the output steps start to vary in size. Red: Ideal Blue: Error Volts Binary Code

Non-Linearity: Differential Typical Causes: resistor network unbalanced binary input voltage values Red: Ideal Blue: Error

Other Types of DACs MOSFET Current Scaling that use a configuration of MOSFETs in a similar manner to R/2R. Voltage Scaled DACs employ a resistor string as a large voltage divider for reference voltage values, and use enable/disable circuitry for the output voltage. Charge Scaling DACs utilize capacitors instead of resistors. Can be more accurate and potentially faster but are more difficult to implement.

END DAC 3 ©Paul R. Godin prgodin°@ gmail.com