SLAAE46 Application note

SLAAE46 November 2021 DAC43701

3.1 Design Note

For this design, the gain required should be:

Equation 4.

G_{V} = (- \frac{R_{3}}{R_{1}}) = (\frac{V_{C O M +} - V_{C O M -}}{V_{D A C +} - V_{D A C -}}) = 5

And the bias voltage should be:

Equation 5.

V_{B I A S} = \frac{R_{5}}{R_{4} + R_{5}} \times V_{E E} = - \frac{V_{D A C +} + V_{D A C -}}{2} = - 1.2 V

Select reasonable resistance values for R₃ and R₅

Equation 6.

R_{3} = 50 k Ω, R_{5} = 4.7 k Ω

From Equation 4 through Equation 6, the required R₁ and R₄ can be calculated.

Equation 7.

R_{1} = R_{2} = 10 k Ω, R_{4} \approx 42.2 k Ω

Some parameters should be checked to make the circuits stable and robust.

Calculate the small signal circuit bandwidth using Equation 8 to ensure it is greater than the 140Hz requirement.

Equation 8.

B W = \frac{{G B}_{O P A 2170}}{N G} = \frac{1.2 M H z}{1 + \frac{R_{3}}{R_{1} | | R_{2}}} = 109 k H z

Where, NG is the noise gain of the inverting summer circuit.

Calculate the minimum slew rate required using Equation 9.

Equation 9.

S R > 2 \times π \times f_{s q u a r e} \times V_{C O M +} = 4.4 m V / μ s

The slew rate of OPA2170 is 0.4V/µs which meets the requirements.

For better stability, the zero created by the gain setting resistors and input capacitance of the OPA2170 should be greater than the bandwidth calculated in Equation 8.

Equation 10.

f_{z e r o} = \frac{1}{2 \times π \times (C_{c m} + C_{d i f f}) \times (R_{1} | | R_{2} | | R_{3})} = 5.8 M H z > = 109 k H z

Where, C_cm and C_diff are the common-mode input capacitance and differential input capacitance of the OPA2170 respectively.