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

3.1 Non-Inverting Measurement

Figure 3-1 shows a test circuit used to measure THD + N of the non-inverting buffer 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 are amplified by the noise gain of the amplifier configuration. When referring to
THD + N measurements, noise gain is sometimes called distortion gain or THD + N gain, and is not equal to the signal gain.

Figure 3-1 Non-Inverting Buffer Distortion Test Circuit

Figure 3-2 Gaining Op Amp THD + N Above Distortion Analyzer Noise Floor

Superposition is used to derive separate equations for the signal gain and the distortion gain. 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 3-1 can be observed as a buffer as shown in Figure 3-3. Therefore the signal gain is $1 \frac{V}{V}$ and the output voltage is equal to the input voltage, as described by Equation 4. 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 3-3 Signal Gain

Equation 4.

V_{o u t} = V_{i n}

Assuming the input signal to the amplifier V_in = 0 V, the amplifier can be observed as a standard non-inverting amplifier with voltages V_os + V_n applied at the non-inverting terminal as shown in Figure 3-4. Therefore V_os + V_n appear on the output amplified by the familiar non-inverting gain equation of one plus the ratio of resistor R_F to resistor R_A. Equation 5 describes the THD + N gain.

Figure 3-4 THD + N Gain

Equation 5.

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

The signal observed at the output of the test circuit shown in Figure 3-1 is the amplified combination of V_in, V_n and V_os. Combining Equation 4 with Equation 5 results in Equation 6, the final gain equation of the test circuit shown in Figure 3-1.

Equation 6.

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

A typical non-inverting buffer application 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 and R_A resulting in gain values for both the test circuit and application circuit . With the assigned resistor values in Table 3-2 the THD + N gain is $101 \frac{V}{V}$ with the additional R_A resistor. In the typical non-inverting buffer circuit R_A = $\infty$ , or in other words doesn't exist and the THD + N gain is $1 \frac{V}{V}$ . Therefore R_A added an additional $101 \frac{V}{V}$ or approximately 40 dB of distortion gain.

Table 3-1 Test Circuit and Application Circuit Gain Values

Condition	Signal Gain	THD + N Gain	R_F	R_A
Signal and THD + N Gain with R_A	$1 \frac{V}{V}$	$101 \frac{V}{V}$	10 kΩ	100 Ω
Signal and THD + N Gain without R_A	$1 \frac{V}{V}$	$1 \frac{V}{V}$	10 kΩ	$\infty$

Figure 3-5 shows the measured THD + N ratio of the OPA1656 in units of decibels. 40 dB is subtracted from the test circuit measurement and represents the actual op amp THD + N for a non-inverting buffer circuit. The measurement bandwidth of the distortion analyzer is 80 kHz for the measurements made in this application note.

Figure 3-5 Non-Inverting Buffer Distortion Measurement: Output Referred

Amplifier data sheets often represent the THD + N ratio in terms of percentage. Equation 7 is used to convert the measured THD + N ratio from dB to percentage.

Equation 7.

T H D + N (%) = 100 \times 10^{\frac{T H D + N (d B)}{20}}

Figure 3-6 shows the THD + N (%) Ratio vs Output Amplitude (V_RMS) for the non-inverting buffer configuration. 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 3-6 Non-Inverting Buffer THD + N (%) Ratio vs Output Amplitude