Transimpedance strikes again: Current-to-voltage conversion with MDACs

Multiplying DACs (MDACs) and their postamplifiers bridge the digital and analog worlds. MDACs generate a current proportional to an input digital code (Figure 1). The postamplifier converts the DAC’s current-output signal to a voltage level. A simple current-to-voltage conversion seems easy to implement with a DAC, amplifier, and resistor. However, this circuit presents stability issues.

For the application, the output model of the MDAC contains a variable current source, resistor, and capacitor (Figure 1a). The value of the output resistance and capacitance depends on the input code to the DAC. In general, programming the MDAC to zero scale causes the output resistance, R_D, to be near infinite. When you program the DAC to full-scale or all ones, this resistance is equal to the feedback resistance, R_F. (See the manufacturer’s data sheets.) The DAC’s output capacitance, C_D, also varies with input code according to the number of internal gate-source junctions across the MDAC output. At full-scale, the MDAC output capacitance equals the data-sheet specification. At zero, the MDAC output capacitance is equal to about half the full-scale value. For stability calculations, use the full-scale output values of R_D and C_D.

The second subnetwork is the amplifier-feedback network. To maintain precision, most MDACs have a feedback resistor on-chip. The feedback capacitor, C_F, is discrete.

In this system, total capacitance at the amplifier input is equal to C_IN=C_D+C_DIF+C_CM. In Figure 1b and Figure 1c, the closed-loop zero is equal to f₁=1/(2π(C_IN+C_F)(R_D||R_F)). The closed-loop pole is equal to f₂=1/(2πC_FR_F).

You ensure system stability if the rate of closure between the open- and closed-loop-gain curve equals 20 dB/decade. To do so, select an amplifier with unity-gain bandwidth of less than f₁ or greater than f₂.

It is easy to design a stable circuit if f₁ is higher than the amplifier’s bandwidth:

Alternatively, if f₂ is lower than the intersection of the open- and the closed-loop-gain curve, use:

C_F≤–C_IN+1/(2/π(R_F||R_D)f_U).

Use these calculated values of feedback capacitance as starting points for your test circuit. Circuit parasitics, device-manufacturing variations, and other factors can encourage you to modify the feedback-capacitor value.

Stabilizing the MDAC’s analog signal is critical. However, also consider amplifier noise, input bias current, offset voltage, MDAC resolution, and glitch energy.