SBOA580 Application note

SBOA580 November 2023 INA1620 , OPA1602 , OPA1604 , OPA1611 , OPA1612 , OPA1612-Q1 , OPA1622 , OPA1632 , OPA1655 , OPA1656 , OPA209 , OPA210 , OPA211 , OPA211-EP , OPA2209 , OPA2210 , OPA2211-EP , OPA2211-HT , OPA2211A

3.2 Inverting Measurement

Figure 3-7 shows a test circuit used to measure THD + N of the inverting amplifier configuration. The input signal V_in to the amplifier is provided by the generator output. The input offset voltage V_os and the input voltage noise V_n are series error sources internal to the op-amp. V_os and V_n are always referred to the non-inverting terminal and both are amplified by the noise gain of the amplifier configuration.

Figure 3-7 Inverting Distortion Test Circuit

Superposition is used to derive separate equations for the signal gain and the distortion gain of the inverting distortion test circuit shown in Figure 3-7. Assuming the input offset voltage V_os = 0 V, the noise voltage V_n = 0 V, and the current i_RA = 0 A the amplifier configuration shown in Figure 3-7 can be viewed as the standard inverting amplifier configuration as shown in Figure 3-8. The signal gain magnitude is determined by the ratio of resistor R_F to resistor R_B. Equation 8 represents the signal gain of the inverting distortion test circuit. The concept of a virtual short is assumed when removing resistor R_A. The voltage potential across resistor R_A on the inverting and non-inverting terminals are equal when applying the concept of a virtual short and therefore i_RA = 0 A and R_A is viewed as an open.

Figure 3-8 Inverting Signal Gain

Equation 8.

V_{o u t} = - V_{i n} \times \frac{R_{F}}{R_{B}}

Figure 3-9 represents the THD + N gain circuit. Assuming V_in = 0 V, resistors R_A and R_B are in parallel. The amplifier can be observed as a standard non-inverting amplifier with the addition of resistor R_A. The voltages V_os + V_n are applied at the non-inverting terminal. V_os + V_n appear at the output gained up by the familiar non-inverting gain equation of one plus the ratio of resistor R_F to R_A|| R_B. Equation 9 represents the THD + N gain of the inverting distortion test circuit.

Figure 3-9 Inverting THD+N Gain

Equation 9.

V_{o u t} = (V_{o s} + V_{n}) (\frac{R_{F}}{R_{A} | | R_{B}} + 1)

Equation 10 is found by expanding Equation 9.

Equation 10.

V_{o u t} = (V_{o s} + V_{n}) (\frac{R_{F}}{R_{A}} + \frac{R_{F}}{R_{B}} + 1)

The signal observed on the output of the test circuit shown in Figure 3-7 is the amplified combination of V_in, V_n and V_os and is represented by Equation 11. Equation 11 represents the final gain equation of the inverting distortion test circuit shown in Figure 3-7.

Equation 11.

V_{o u t} = - V_{i n} \times \frac{R_{F}}{R_{B}} + (V_{o s} + V_{n}) (\frac{R_{F}}{R_{A}} + \frac{R_{F}}{R_{B}} + 1)

The typical inverting circuit does not include the additional resistor R_A. Resistor R_A was added to the test circuit to provide additional gain for the purpose of overcoming the signal analyzer measurement limitation. Table 3-2 assigns values to resistors R_F, R_A and R_B and the associated gain values for both the test circuit and application circuit are calculated. With the assigned resistor values in Table 3-2 the THD + N gain is $102 \frac{V}{V}$ with the addition of resistor R_A. In the common inverting application circuit R_A = $\infty$ , or in other words doesn't exist and the
THD + N gain is $2 \frac{V}{V}$ . Therefore R_A added an additional $51 \frac{V}{V}$ or approximately 34 dB of distortion gain.

Table 3-2 Test Circuit and Application Circuit Gain Values

Condition	Signal Gain	THD + N Gain	R_F	R_A	R_B
Signal & THD + N Gain with R_A	$-1 \frac{V}{V}$	$102 \frac{V}{V}$	10 kΩ	100 Ω	10 kΩ
Signal & THD + N Gain without R_A	$-1 \frac{V}{V}$	$2 \frac{V}{V}$	10 kΩ	$\infty$	10 kΩ

Figure 3-10 shows the measured THD + N ratio of the OPA1656 in units of decibels. 34 dB is subtracted from the test circuit measurement and represents the actual op amp THD + N that is seen in the typical inverting circuit. The measurement bandwidth of the distortion analyzer is 80 kHz.

Figure 3-10 Inverting Distortion Measurement: Output Referred

Figure 3-11 shows the THD + N (%) ratio vs Output Amplitude (V_RMS) for the common inverting application circuit. Two independent measurements were made for 1 kHz and 20 kHz frequencies as the output amplitude was swept from 0.1 V_RMS to 10 V_RMS.

Figure 3-11 Inverting THD + N (%) Ratio vs Output Amplitude