Input Impedance of Op Amp: What It Is and How to Calculate It

What is Input Impedance?

Input impedance refers to the effective resistance and capacitance that an op amp presents to the signal source connected to its input terminals. It is a measure of the op amp’s ability to resist the flow of current into its inputs. A high input impedance is desirable as it minimizes the loading effect on the signal source and ensures that the op amp does not significantly alter the characteristics of the input signal.

Ideal vs. Real Op Amp Input Impedance

In an ideal op amp, the input impedance is considered to be infinite, meaning that no current flows into the op amp’s inputs. However, practical op amps have finite input impedance values. The input impedance of a real op amp is typically very high, in the range of several megaohms or even teraohms, but it is not infinite.

Significance of Input Impedance in Op Amp Circuits

The input impedance of an op amp plays a vital role in various circuit configurations. Let’s explore some common scenarios where input impedance is crucial:

Voltage Follower (Buffer) Configuration

In a voltage follower configuration, the op amp’s output is directly connected to its inverting input, creating a unity-gain buffer. The input impedance of the op amp determines the loading effect on the signal source. A high input impedance ensures that the buffer does not draw significant current from the source, preserving the integrity of the input signal.

Inverting and Non-Inverting Amplifier Configurations

In inverting and non-inverting amplifier configurations, the input impedance of the op amp affects the overall gain and frequency response of the circuit. The input impedance forms a voltage divider with the external feedback resistors, influencing the signal attenuation at the input stage. A high input impedance minimizes the loading effect and maintains the desired gain characteristics.

Summing Amplifier Configuration

In a summing amplifier configuration, multiple input signals are combined at the inverting input of the op amp. The input impedance determines the degree of isolation between the input signals. A high input impedance prevents the input signals from interfering with each other and ensures accurate summing of the signals.

Calculating Input Impedance

To calculate the input impedance of an op amp, we need to consider both the differential and common-mode input impedances. The differential input impedance is the impedance between the inverting and non-inverting inputs, while the common-mode input impedance is the impedance from each input to ground.

Differential Input Impedance

The differential input impedance (Zid) of an op amp is typically specified in the op amp’s datasheet. It is usually modeled as a resistor (Rid) in parallel with a capacitor (Cid). The differential input impedance can be calculated using the following formula:

Zid = Rid || (1 / (2πfCid))

where:
– Rid is the differential input resistance
– Cid is the differential input capacitance
– f is the frequency of the input signal

For example, let’s consider an op amp with a differential input resistance (Rid) of 10 MΩ and a differential input capacitance (Cid) of 5 pF. To calculate the differential input impedance at a frequency of 1 kHz, we can use the formula:

Zid = 10 MΩ || (1 / (2π × 1 kHz × 5 pF))
Zid ≈ 9.97 MΩ

Common-Mode Input Impedance

The common-mode input impedance (Zic) of an op amp is also specified in the datasheet. It represents the impedance from each input terminal to ground and is typically modeled as a resistor (Ric) in parallel with a capacitor (Cic). The common-mode input impedance can be calculated using the following formula:

Zic = Ric || (1 / (2πfCic))

where:
– Ric is the common-mode input resistance
– Cic is the common-mode input capacitance
– f is the frequency of the input signal

For example, if an op amp has a common-mode input resistance (Ric) of 100 MΩ and a common-mode input capacitance (Cic) of 3 pF, the common-mode input impedance at a frequency of 10 kHz can be calculated as:

Zic = 100 MΩ || (1 / (2π × 10 kHz × 3 pF))
Zic ≈ 99.5 MΩ

Impact of Input Impedance on Circuit Performance

The input impedance of an op amp can have significant implications on circuit performance. Here are a few key aspects to consider:

Bandwidth and Frequency Response

The input impedance of an op amp, particularly the input capacitance, forms a low-pass filter with the source impedance. This can limit the bandwidth and affect the frequency response of the circuit. To maintain a wide bandwidth, it is crucial to choose an op amp with low input capacitance and ensure that the source impedance is relatively low compared to the input impedance.

Noise Performance

The input impedance of an op amp can influence its noise performance. A high input impedance op amp is generally preferred for low-noise applications. However, it is essential to consider the trade-off between input impedance and input bias current. Op amps with extremely high input impedances may have higher input bias currents, which can introduce additional noise.

Input Bias Current and Offset Voltage

The input impedance of an op amp is closely related to its input bias current and offset voltage. Input bias current is the small current that flows into or out of the op amp’s input terminals to bias the input stage. A high input impedance op amp typically has lower input bias currents, which is desirable for minimizing input offset voltages and preserving signal integrity.

Techniques to Increase Input Impedance

In some applications, it may be necessary to increase the input impedance of an op amp circuit beyond the inherent input impedance of the op amp itself. Here are a few techniques that can be employed:

Input Bias Current Compensation

Input bias current compensation techniques involve adding external components to compensate for the input bias current of the op amp. One common method is to use a resistor in series with the non-inverting input, equal in value to the parallel combination of the feedback resistor and the source impedance. This helps to cancel out the effect of input bias current and increase the effective input impedance.

Bootstrapping

Bootstrapping is a technique that involves applying a portion of the output signal back to the input stage to effectively increase the input impedance. By feeding back the output signal, the input stage sees a reduced voltage difference, which in turn reduces the input current and increases the apparent input impedance. Bootstrapping can be implemented using additional op amp stages or discrete components.

Guarding

Guarding is a technique used to minimize leakage currents and increase the effective input impedance in high-impedance circuits. It involves surrounding the high-impedance input node with a conductive shield that is driven by a low-impedance source, such as the output of a unity-gain buffer. The guard shield helps to reduce the effects of Stray Capacitance and leakage currents, effectively increasing the input impedance.

Frequently Asked Questions (FAQ)

1. Q: What is the typical input impedance of an op amp?
   A: The input impedance of an op amp can vary depending on the specific device and its architecture. However, most modern op amps have input impedances in the range of several megaohms to tens of megaohms, with some high-impedance op amps reaching input impedances of hundreds of megaohms or even teraohms.

2. Q: Why is high input impedance desirable in op amp circuits?
   A: High input impedance is desirable because it minimizes the loading effect on the signal source connected to the op amp’s inputs. It ensures that the op amp does not draw significant current from the source, preserving the integrity of the input signal. High input impedance also helps to maintain the desired gain and frequency response characteristics of the circuit.

3. Q: Can the input impedance of an op amp vary with frequency?
   A: Yes, the input impedance of an op amp can vary with frequency due to the presence of input capacitance. The input impedance decreases as the frequency increases because the reactance of the input capacitance becomes lower at higher frequencies. This can limit the bandwidth and affect the frequency response of the circuit.

4. Q: How does input impedance affect the noise performance of an op amp?
   A: Input impedance can influence the noise performance of an op amp. Generally, op amps with higher input impedances tend to have better noise performance. However, there is a trade-off between input impedance and input bias current. Op amps with extremely high input impedances may have higher input bias currents, which can introduce additional noise. It is important to consider this trade-off when selecting an op amp for low-noise applications.

5. Q: What are some techniques to increase the input impedance of an op amp circuit?
   A: There are several techniques that can be used to increase the input impedance of an op amp circuit beyond the inherent input impedance of the op amp itself. These techniques include input bias current compensation, bootstrapping, and guarding. Input bias current compensation involves adding external components to compensate for the input bias current. Bootstrapping involves applying a portion of the output signal back to the input stage to effectively increase the input impedance. Guarding involves surrounding the high-impedance input node with a conductive shield driven by a low-impedance source to reduce leakage currents and increase the effective input impedance.

Conclusion

Input impedance is a crucial characteristic of op amps that determines how they interact with the circuitry connected to their inputs. A high input impedance is desirable to minimize loading effects, preserve signal integrity, and maintain the desired gain and frequency response characteristics. Understanding the concept of input impedance, its significance in various op amp configurations, and how to calculate it is essential for designing robust and efficient op amp circuits.

By considering factors such as differential and common-mode input impedances, the impact on bandwidth and noise performance, and techniques to increase input impedance, designers can optimize their op amp circuits for specific applications. With a solid grasp of input impedance and its implications, engineers can unleash the full potential of op amps in a wide range of analog electronic systems.