# The inner workings of the three-op-amp INA

The standard varieties of INAs come with two or three internal operational amplifiers (op amps). In this article, we look at the three-op amp variety (Figure 1).

*Figure 1: A three-op-amp instrumentation amplifier using the INA333.*

The three op amps in Figure 1 are A1, A2 and A3. Several variables influence the successful operation of this INA. These variables are VDD, VSS, VREF, RG, VCM, and VDIFF. This seems like a lot of balls to juggle, but the ‘hidden’ nodes that warrant special attention are the A1 and A2 output nodes: VOA1 and VOA2. A1 and A2 in combination with RG implement the gain of this INA, while A3 converts the differential signal into a single-ended output.

So let’s just jump in and see what happens. If a single power supply configuration is applied to the INA, for example, VDD = 5V and VSS = 0V, VCM and VREF are equal to (VDD – VSS) / 2. In our configuration RG = 1.01 kΩ, which creates a gain of 100. In our circuit example, we keep VDD = 5V, VSS = 0V, and VCM = 2.5V as above, but make the value of VREF equal to ground, or 0V. This VREF voltage conveniently reduces our chip count by removing the need for a voltage reference IC chip.

Let’s try this circuit out. When I provide a differential +2 mV DC input signal between the VIN+ and VIN– pins (VDIFF), the output (VOUT) becomes 0.2V, giving a gain of 100 V/V. But, when VDIFF equals –2 mV, the output becomes 0.1V (gain = 50 V/V).

With this circuit configuration, let’s apply VDIFF input of +60 mV. At the bench, the output that appears on the output pin is 4.85V. This equates to a gain of ~81 V/V. The value of 4.85V is not high enough to indicate that A3 is overdriven. Is it true that this INA’s gain is unstable?

*next; what’s really going on?…*

Should I look for another INA in hopes of finding a stable one? Or better yet, figure out what is happening? In Figure 2, there is a generic list of critical internal relationships and formulae using the INA333. For a three-op-amp INA, these formulae will apply with the exception of the 100 mV and 75 mV values in the right column. These numeric values represent the limitations of the VOA1, VOA2, and VOUT stages.

*Figure 2 Critical internal node relationships and formulas for the INA333.*

The critical node equations in the left column of Figure 2 describe values of five nodes. For our three-op-amp INA application, the values of these nodes are:

VIN+ = 2.5V + 60 mV / 2 = 2.53V

VIN– = 2.5V – 60 mV / 2 = 2.47V

For future reference, we calculate the internal output voltages of A1 and A2. The input signals, VIN+ and VIN–, go to the outputs of A1 and A2 provide these output voltages:

VOA1 = 2.5V – (60 mV / 2) (1 + 100k / 1.01k) = –0.5V

VOA2 = 2.5V + (60 mV / 2) (1 + 100k / 1.01k) = 5.5V

The output voltage of this INA circuit combines the reference voltage at the non-inverting input of A3 and the gained input signals (VIN+, VIN–).

VOUT = 0V + (2.53V – 2.47V)(1 + 100k / 1.01k) = 6V

These equations provide a good, theoretical transfer function of the signals through this INA circuit. But, let’s look at reality for a minute.

*next; internal amp behaviour…*

Be aware of the output swing limitations of these three internal amplifiers. The right column in Figure 2 describes the capability of A1 and A2 output swing. According to these formulae, VOA1 and VOA2 will range approximately from VSS +75 mV to VDD – 75 mV, or with our supplies 75 mV to 4.925V. Note that our theoretical values for VOA1 and VOA2 are –0.5V and 5.5V. In reality, VOA1 is approximately equal to 75 mV, and VOA2 is approximately equal to 4.925V. These two voltages travel through the difference amplifier, A3, where VOA2 – VOA1 = VOUT, which is approximately equal to 4.85V.

From the right column of Figure 2, you can see that the approximate swing capability of A3 is VSS +75 mV to VDD – 75 mV. Again, with our supplies the output voltage range is 75 mV to 4.925V. Given these limits and our previous calculations of VOA1 and VOA2 values it is obvious that the output range of this INA is limited internally by A1 and A2.

*Figure 3: Typical common-mode range vs output voltage with the INA333.*

Figure 3 describes the relationship between the common-mode voltage (VCM) and the INA’s output pin (VOUT). All other variables such as supply voltages, voltage reference, and circuit gain, are given.

In Figure 3, note the red circle on the right middle side of this diagram. The lines within this circle verify that the amplifier will not be able to reach the output voltage of 5V. The limitations in this circuit are the internal amplifiers: A1 and A2. Any and all three-op-amp INAs have these types of limitations.

It is easy to overdrive A1 and A2 without knowing it. There are no external indicators to notify the occurrence of this condition. So how do you solve this problem? In this instance, I recommend that you centre VREF in the middle of the supplies or 2.5V. If you do this, you will have great success!

**References **

1. Nastase, Adrian S, How to Derive the Instrumentation Amplifier Transfer Function, Mastering Electronic Design

2. TI E2E Community, Precision Amplifier Forum, Texas Instruments

3. INA333 product folder, Texas Instruments