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

**Figure 1**).

The three op amps in

**Figure 1**are A

_{1}, A

_{2}and A

_{3}. Several variables influence the successful operation of this INA. These variables are V

_{DD}, V

_{SS}, V

_{REF}, R

_{G}, V

_{CM}, and V

_{DIFF}. This seems like a lot of balls to juggle, but the ‘hidden’ nodes that warrant special attention are the A

_{1}and A

_{2}output nodes: V

_{OA1}and V

_{OA2}. A

_{1}and A

_{2}in combination with R

_{G}implement the gain of this INA, while A

_{3}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, V

_{DD}= 5V and V

_{SS}= 0V, V

_{CM}and V

_{REF}are equal to (V

_{DD}– V

_{SS}) / 2. In our configuration R

_{G}= 1.01 kOhms, which creates a gain of 100. In our circuit example, we keep V

_{DD}= 5 V, V

_{SS}= 0V, and V

_{CM}= 2.5V as above, but make the value of V

_{REF}equal to ground, or 0V. This V

_{REF}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 V

_{IN+}and V

_{IN–}pins (V

_{DIFF}), the output (V

_{OUT}) becomes 0.2 V, giving a gain of 100 V/V. But, when V

_{DIFF}equals –2 mV, the output becomes 0.1V (gain = 50 V/V).

With this circuit configuration, let’s apply V

_{diff}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?

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 formulas using the INA333. For a three-op-amp INA, these formulas 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 V

_{OA1}, V

_{OA2}, and V

_{OUT}stages.

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:

_{IN+}= 2.5V + 60 mV / 2 = 2.53V

V

_{IN–}= 2.5V - 60 mV / 2 = 2.47V

For future reference, we calculate the internal output voltages of A1 and A2. The input signals, V

_{IN+}and V

_{IN–}, go to the outputs of A

_{1}and A

_{2}provide these output voltages:

_{OA1}= 2.5V – (60 mV / 2) (1 + 100k / 1.01k) = –0.5V

V

_{OA2}= 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 A

_{3}and the gained input signals (V

_{IN+}, V

_{IN–}).

_{OUT}= 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.

Be aware of the output swing limitations of these three internal amplifiers. The right column in

**Figure 2**describes the capability of A

_{1}and A

_{2}output swing. According to these formulas, V

_{OA1}and V

_{OA2}will range approximately from V

_{SS}+75 mV to V

_{DD}– 75 mV, or with our supplies 75 mV to 4.925 V. Note that our theoretical values for V

_{OA1}and V

_{OA2}are –0.5 V and 5.5 V. In reality, V

_{OA1}is approximately equal to 75 mV, and V

_{OA2}is approximately equal to 4.925 V. These two voltages travel through the difference amplifier, A3, where V

_{OA2}– V

_{OA1}= V

_{OUT}, which is approximately equal to 4.85 V.

From the right column of

**Figure 2**, you can see that the approximate swing capability of A

_{3}is V

_{SS}+75 mV to V

_{DD}– 75 mV. Again, with our supplies the output voltage range is 75 mV to 4.925 V. Given these limits and our previous calculations of V

_{OA1}and V

_{OA2}values it is obvious that the output range of this INA is limited internally by A

_{1}and A

_{2}.

**Figure 3**describes the relationship between the common-mode voltage (Vcm) and the INA’s output pin (V

_{OUT}). All other variables such as supply voltages, voltage reference, and circuit gain, are given.

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

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: A

_{1}and A

_{2}. Any and all three-op-amp INAs have these types of limitations.

It is easy to overdrive A

_{1}and A

_{2}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 center V

_{REF}in the middle of the supplies or 2.5 V. If you do this, you will have great success!

**References**

- Nastase, Adrian S, How to Derive the Instrumentation Amplifier Transfer Function, Mastering Electronic Design
- TI E2E Community, Precision Amplifier Forum, Texas Instruments
- INA333 product folder, Texas Instruments

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