Understanding Open Loop Gain in Op Amp Circuits: Theory, Testing, and Design

The open loop gain in op amp devices (denoted as $A_{OL}$) is the raw, uncorrected voltage amplification factor of the internal transistor stages when no external feedback network is connected. In a modern precision operational amplifier, this number is staggeringly high—typically between 100,000 and 1,000,000 (100 dB to 120 dB). However, because this gain is so high and highly variable with temperature and frequency, we almost never use op-amps in an open-loop configuration for linear amplification. Instead, we apply negative feedback to force the circuit into a predictable closed-loop state.

If you are selecting a part for a new build, here are the safe default part numbers with their typical open-loop gain ratings and maximum supply voltages:

• LM358: General-purpose, single-supply bipolar. $A_{OL}$ ≈ 100 dB (100 V/mV). Max supply: 32V. Cost: ~$0.15.
• TL072: Low-noise audio, dual JFET input. $A_{OL}$ ≈ 114 dB (500 V/mV). Max supply: 36V. Cost: ~$0.40.
• OPA2134: High-precision, dual FET input. $A_{OL}$ ≈ 120 dB (1000 V/mV). Max supply: 36V. Cost: ~$4.50.

Op-Amp Pinout, Symbol, and Operating Regions

Before wiring any feedback network, you must understand the physical pins and the three distinct operating regions dictated by the open loop gain. The standard schematic symbol shows a non-inverting input (+), an inverting input (-), a positive supply rail (V+), a negative supply rail (V-), and an output.

For a standard 8-pin DIP dual op-amp (like the TL072 or OPA2134), the pinout is strictly standardized:

• Pin 1: Output A
• Pin 2: Inverting Input A (-)
• Pin 3: Non-Inverting Input A (+)
• Pin 4: V- (Negative Supply / Ground)
• Pin 5: Non-Inverting Input B (+)
• Pin 6: Inverting Input B (-)
• Pin 7: Output B
• Pin 8: V+ (Positive Supply)

Because $A_{OL}$ is finite but massive, the output voltage ($V_{out}$) is governed by the equation $V_{out} = A_{OL} \times (V_+ - V_-)$. This creates three distinct operating regions:

Why Open Loop Gain Dictates Your Closed-Loop Accuracy

Many hobbyists assume that if they set a closed-loop gain of 10 using resistors, the circuit will amplify by exactly 10. In reality, the finite open loop gain introduces a measurable gain error. According to Texas Instruments Precision Labs, the actual closed-loop gain ($G_{actual}$) is calculated as:

$G_{actual} = \frac{A_{OL}}{1 + \beta A_{OL}}$

Where $\beta$ is the feedback fraction ($\frac{R_i}{R_i + R_f}$). Let us run a concrete numeric example. You want a non-inverting gain of 100 (40 dB). You use $R_f = 99k\Omega$ and $R_i = 1k\Omega$, making $\beta = 0.01$.

• Ideal Gain: $1 + (99k / 1k) = 100$.
• With $A_{OL} = 100,000$ (100 dB): $G_{actual} = \frac{100,000}{1 + (0.01 \times 100,000)} = \frac{100,000}{1001} = 99.9$. The error is a negligible 0.1%.
• With $A_{OL} = 10,000$ (80 dB, typical at 10 kHz): $G_{actual} = \frac{10,000}{1 + (0.01 \times 10,000)} = \frac{10,000}{101} = 99.0$. The error jumps to 1%.

This demonstrates why open loop gain rolls off at higher frequencies due to internal compensation capacitors. If your application requires high accuracy at high frequencies, you must choose an op-amp with a higher Gain-Bandwidth Product (GBWP) so that $A_{OL}$ remains large at your operating frequency.

Practical Application: Designing a Precision Non-Inverting Amplifier

Let us build a precision DC-coupled non-inverting amplifier with a gain of 10 using the OPA2134. This circuit is ideal for buffering and amplifying low-level sensor signals (like strain gauges or thermocouples) where the high 120 dB open loop gain minimizes DC errors.

Bill of Materials:

• 1x OPA2134PA (8-pin DIP)
• 1x $R_f$: 9.09 kΩ, 1% tolerance, 1/4W metal film resistor
• 1x $R_i$: 1.00 kΩ, 1% tolerance, 1/4W metal film resistor
• 2x 100 nF (0.1 µF) X7R MLCC ceramic capacitors
• 1x 10 µF electrolytic capacitor (for bulk supply decoupling)

Assembly and Biasing Steps:

1. Seat the IC: Insert the OPA2134 into the breadboard, straddling the center trench. Ensure the notch faces left (Pin 1 is top-left).
2. Wire Power Rails: Connect Pin 8 to your positive bench supply (+12V) and Pin 4 to the negative supply (-12V). Never exceed the 36V total differential rating.
3. Decouple the Rails: Place a 100 nF ceramic capacitor between Pin 8 and Pin 4, physically located within 2mm of the IC pins. This provides a high-frequency AC ground, preventing the high open loop gain from amplifying power supply noise into high-frequency oscillation.
4. Connect Feedback Network: Connect one end of $R_f$ (9.09k) to Pin 1 (Output A). Connect the other end to Pin 2 (Inverting Input A). This sets the feedback path.
5. Connect Ground Reference: Connect $R_i$ (1.00k) between Pin 2 (Inverting Input A) and circuit ground (0V).
6. Apply Input Signal: Feed your sensor signal into Pin 3 (Non-Inverting Input A) via a shielded coaxial cable to prevent EMI pickup, which the massive $A_{OL}$ will gladly amplify.
7. Verify Output: Measure Pin 1 with a multimeter. A 0.500V input at Pin 3 should yield exactly 5.00V at Pin 1.

Bench Testing: How Op-Amps Fail and Multimeter Diagnostics

Op-amps rarely fail gracefully. As noted in application notes from All About Circuits, the most common failure modes are Electrical Overstress (EOS) blowing the input differential pair, Electrostatic Discharge (ESD) punching through the gate oxide on FET inputs, or shorting the output to a rail and melting the internal bond wires.

Here is how to test a suspected dead op-amp using a standard digital multimeter (DMM):

1. De-energize and Discharge: Remove all power from the circuit and short the power rails together with a 1k resistor to discharge any decoupling capacitors.
2. Input Diode Test: Set your DMM to diode test mode. Place the red probe on the non-inverting input (Pin 3) and the black probe on the inverting input (Pin 2). You should read "OL" (open loop) or a very high impedance. If you read a dead short (0.00V) or a low diode drop in both directions, the input differential pair is blown from EOS.
3. Output Short Check: In continuity mode, check between the Output pin (Pin 1) and both V+ (Pin 8) and V- (Pin 4). You should not have a dead short. A short here indicates a melted output stage bond wire.
4. Power-On Offset Test: Reapply power. Tie both inputs (Pins 2 and 3) directly to ground. Measure the DC voltage at the output pin. In a healthy OPA2134, the output should read within ±5mV of 0V. If the output is slammed against the positive or negative rail (e.g., +11V or -11V), the internal input offset voltage ($V_{os}$) has drifted catastrophically, indicating internal silicon damage.

Frequently Asked Questions About Open Loop Gain

Does open loop gain in op amp circuits change with temperature?

Yes. The open loop gain of bipolar and FET op-amps decreases as the junction temperature rises. For a standard LM358, $A_{OL}$ might be 100 dB at 25°C, but it can drop by 10 dB to 15 dB at 85°C. In precision DC circuits, this thermal drift alters your closed-loop gain accuracy. If your circuit operates in a hot environment (like an automotive engine bay or inside a sealed LED fixture), you must calculate your gain error using the $A_{OL}$ value specified at the maximum ambient temperature in the datasheet, not the 25°C room-temperature value.

Can I use an op-amp in open-loop mode as a comparator?

Technically yes, but it is highly discouraged for anything beyond crude prototyping. When an op-amp is used open-loop, the massive gain forces the output into saturation. When the input crosses zero and you want the output to swing back, the op-amp must recover from saturation. This "overload recovery time" is not specified in most op-amp datasheets and can take several microseconds, causing severe propagation delay. Furthermore, without hysteresis, noise on the input will cause the output to chatter violently. If you need to compare voltages, buy a dedicated comparator IC like the LM393, which is designed to switch rapidly without saturation delay.

How do I measure the open loop gain of an op-amp on my bench?

You cannot simply apply 1mV to the input and measure the output; the gain is so high that the output will instantly saturate against the power rails, and 60Hz mains hum picked up by your test leads will swamp the signal. To measure $A_{OL}$ accurately, engineers use a specialized "servo-loop" test circuit. This involves using a second, high-gain "loop" op-amp to force the Device Under Test (DUT) output to a specific mid-rail voltage while injecting a known AC signal. For most hobbyists and DIYers, measuring open loop gain directly is unnecessary; rely on the manufacturer's Bode plots in the datasheet to see how $A_{OL}$ rolls off across frequency.

Why does open loop gain roll off at higher frequencies?

Op-amps are intentionally designed with a dominant pole—a built-in low-pass filter—to prevent them from oscillating when used with negative feedback. Manufacturers achieve this by integrating a tiny Miller compensation capacitor (typically around 30pF) inside the silicon die. This capacitor forces the open loop gain to roll off at a strict -20 dB per decade starting at a very low frequency (often just 10 Hz). By the time you reach the op-amp's Unity Gain Bandwidth (where $A_{OL}$ drops to 1, or 0 dB), the phase shift is controlled, ensuring your closed-loop circuit remains stable rather than turning into an unintended RF oscillator.