• Voltage amplifiers:
  • Z_in ≫ Z_source (≥10×)
  • Z_out ≪ Z_load (≤0.1×)
• Current amplifiers:
  • Z_in ≪ Z_source
  • Z_out ≫ Z_load

Measurement Techniques

For experimental characterization:

1. Input impedance:
   1. Insert a known resistor R_test in series with the input
   2. Measure the voltage divider effect: Z_in = R_test/(V_source/V_in - 1)
2. Output impedance:
   1. Measure open-circuit output voltage V_oc
   2. Measure loaded voltage V_L with known load R_L
   3. Calculate: Z_out = R_L(V_oc/V_L - 1)

Frequency Dependence

Both impedances vary with frequency due to:

• Parasitic capacitances (input capacitance C_in, output capacitance C_out)
• Inductive effects at high frequencies
• Feedback network impedance variations

For a common-emitter amplifier, the input impedance includes:

Practical Design Implications

In RF systems, the reflection coefficient Γ quantifies impedance mismatch:

Modern amplifiers often incorporate:

• On-chip termination resistors (e.g., 50Ω for RF systems)
• Active impedance control circuits
• Balun transformers for impedance transformation

The input impedance of an amplifier, denoted as Z_in, critically determines how effectively signal power transfers from a source to the amplifier. A mismatch between the source impedance Z_s and Z_in results in signal reflection and power loss, governed by the reflection coefficient Γ:

When Z_in = Z_s (impedance matching), Γ = 0, ensuring maximum power transfer. For voltage-sensitive circuits, however, a high Z_in (≫ Z_s) minimizes loading effects, preserving signal amplitude. Conversely, current-sensitive systems benefit from low Z_in to avoid current division losses.

Practical Implications in Circuit Design

In RF systems, 50 Ω or 75 Ω input impedances are standardized to match transmission lines, reducing standing waves. For audio amplifiers, Z_in ≥ 10× the source impedance (e.g., 10 kΩ for a 1 kΩ microphone) ensures negligible voltage drop. Consider a source with V_s = 1 V and Z_s = 600 Ω driving an amplifier:

With Z_in = 10 kΩ, V_in ≈ 0.94 V (6% loss), whereas Z_in = 600 Ω yields V_in = 0.5 V (50% loss).

Frequency Dependence and Parasitics

At high frequencies, parasitic capacitance (C_in) and inductance alter Z_in. For instance, a 1 pF capacitance at 100 MHz introduces an impedance of:

This reactive component can cause phase shifts and frequency-dependent attenuation, necessitating careful PCB layout and shielding.

Case Study: Oscilloscope Probes

10× passive probes use a 9 MΩ resistor in series with the oscilloscope's 1 MΩ input impedance, forming a 10:1 voltage divider. The probe's compensation capacitor adjusts for high-frequency roll-off, ensuring flat response. Mismatched probes introduce artifacts like ringing or attenuation, as seen in the step response below:

Voltage Divider Method

The most straightforward approach uses a series resistor (R_s) and measures the voltage drop across the amplifier input. When a known signal source (V_in) is applied, the input impedance (Z_in) forms a voltage divider with R_s:

where V_amp is the voltage at the amplifier input. This method assumes Z_in is purely resistive. For complex impedances, phase-sensitive measurements are required.

Network Analyzer Technique

Vector network analyzers (VNAs) provide the most accurate characterization by measuring the reflection coefficient (Γ) at the input port:

where Z₀ is the reference impedance (typically 50Ω). A VNA sweeps frequency to capture impedance variations across the bandwidth of interest, including reactive components.

Current Injection Method

For high-impedance circuits (>1MΩ), injecting a known AC current (I_test) through a coupling capacitor avoids loading effects. The input impedance is derived from:

This technique is particularly useful for measuring the input impedance of operational amplifiers or instrumentation amplifiers where traditional methods may introduce significant errors.

Time-Domain Reflectometry (TDR)

TDR methods analyze reflected step pulses to determine impedance discontinuities. The input impedance is calculated from the reflection amplitude (ρ):

TDR provides nanosecond-scale resolution, making it ideal for characterizing transmission line effects in RF amplifiers. Modern oscilloscopes with TDR capabilities can automate this measurement.

Practical Considerations

• Frequency dependence: Always specify the measurement frequency as Z_in varies with operating conditions.
• Bias conditions: Active devices exhibit different input impedances under DC bias versus small-signal conditions.
• Parasitic effects: Stray capacitances and lead inductances become significant at high frequencies (>100MHz).

Calibration Requirements

All measurement techniques require proper calibration to remove systematic errors. For RF measurements, this includes:

• Open/short/load calibration for one-port measurements
• Through calibration for two-port measurements
• De-embedding of test fixtures when necessary

Network Analyzers

Vector Network Analyzers (VNAs) are indispensable for measuring the input impedance of amplifiers across a wide frequency range. These instruments operate by injecting a known signal into the amplifier's input and measuring the reflected wave, allowing the calculation of the reflection coefficient (Γ). The input impedance (Z_in) is then derived from:

where Z₀ is the characteristic impedance of the system (typically 50 Ω). Modern VNAs, such as the Keysight PNA series, offer high dynamic range (>120 dB) and phase accuracy (<0.1°), enabling precise measurements even for high-impedance or low-loss networks.

Impedance Analyzers

For lower frequency applications (DC to ~50 MHz), impedance analyzers like the Keysight E4990A provide direct measurement of complex impedance (Z = R + jX). These instruments use auto-balancing bridge techniques to eliminate lead resistance effects, achieving accuracies of ±0.05% for impedance magnitudes from 1 mΩ to 100 MΩ. The measurement principle involves:

where R_ref is a precision reference resistor. This method is particularly effective for characterizing input impedance variations with DC bias in transistor amplifiers.

Oscilloscope-Based Methods

When high-frequency network analyzers are unavailable, a time-domain reflectometry (TDR) approach using fast-edge pulse generators and high-bandwidth oscilloscopes can be employed. The input impedance is calculated from the reflected voltage waveform:

Modern sampling oscilloscopes (e.g., Tektronix DPO70000SX) with >70 GHz bandwidth and <200 fs jitter enable impedance measurements with sub-nanosecond temporal resolution. This technique is particularly valuable for troubleshooting impedance discontinuities in amplifier input networks.

Signal Generators and Power Meters

A classic substitution method involves using a calibrated signal generator and RF power meter. The amplifier input is terminated with variable precision loads while monitoring forward power. The input impedance corresponds to the load value yielding maximum power transfer (minimum reflection). This approach, while less precise than VNA methods, remains useful for quick verification in field applications where:

High-quality signal generators (e.g., Rohde & Schwarz SMA100B) with <-110 dBc harmonic distortion ensure minimal measurement contamination from spurious signals.

Practical Considerations

When measuring amplifier input impedance, several systematic errors must be mitigated:

• Cable phase delay: For frequencies above 1 GHz, even 10 cm of coaxial cable can introduce significant phase shift (≈36° at 5 GHz in RG-58).
• Fixturing parasitics: Test fixtures contribute stray capacitance (typically 0.1-1 pF) and inductance (0.5-5 nH) that must be de-embedded.
• Thermal drift: Semiconductor amplifiers exhibit impedance variations of 0.1-0.5%/°C, necessitating temperature stabilization during measurements.

Advanced calibration techniques such as Short-Open-Load-Thru (SOLT) or Thru-Reflect-Line (TRL) are essential for VNA measurements, reducing systematic errors to <0.1 dB in magnitude and <1° in phase up to 40 GHz.

Non-Ideal Source Impedance Effects

The theoretical input impedance Z_in assumes an ideal voltage source. In practice, the source impedance Z_S forms a voltage divider with the amplifier's input impedance, modifying the effective gain. The actual input voltage V_in becomes:

For minimal signal attenuation, Z_in should satisfy Z_in ≫ Z_S (typically by a factor of 10 or more). This becomes critical in high-frequency applications where transmission line effects introduce complex impedance components.

Frequency-Dependent Behavior

At high frequencies, parasitic capacitances dominate input impedance characteristics. The small-signal model reveals:

where C_in includes both intentional and parasitic capacitances. This leads to a roll-off in input impedance magnitude with frequency:

Above the pole frequency f_p = 1/(2πR_inC_in), the input impedance decreases at 20 dB/decade. This effect is particularly pronounced in FET-input amplifiers due to their high R_in and significant gate capacitance.

Bias Network Interactions

DC bias networks often introduce unexpected impedance paths. A common-emitter amplifier's input impedance is modified by the base-bias resistors:

where r_e = V_T/I_C. The parallel combination of bias resistors can dominate the input impedance, especially in low-power designs where (β+1)r_e is large. This creates a design trade-off between bias stability and input impedance requirements.

Thermal and Nonlinear Effects

In power amplifiers, input impedance varies with:

• Temperature: Semiconductor junction resistances change approximately 0.5%/°C
• Signal level: Large signals modulate base-emitter/gate-source capacitances
• Operating point: BJT input impedance varies with collector current as r_π = β/g_m

These effects introduce harmonic distortion and intermodulation products when driving nonlinear impedances.

Measurement Challenges

Common impedance measurement pitfalls include:

• Probe loading: 10X oscilloscope probes typically present 10 MΩ || 10 pF
• Ground loop errors: Improper grounding creates parallel impedance paths
• Network analyzer calibration: Reference plane errors in VNA measurements

The most accurate method uses a series resistor and voltage divider measurement:

with R_series chosen to be comparable to the expected Z_in for optimal sensitivity.

Fundamental Considerations

The input impedance of an amplifier is a critical parameter that determines how effectively it interfaces with preceding stages or signal sources. Unlike idealized models, real-world amplifiers exhibit input impedance influenced by their topology—common-emitter (CE), common-source (CS), common-collector (CC), or common-drain (CD). Each configuration presents distinct impedance characteristics due to intrinsic device physics and biasing conditions.

Bipolar Junction Transistor (BJT) Topologies

In a common-emitter amplifier, the input impedance is primarily governed by the transistor's base-emitter junction resistance (r_π) and the biasing network. For small-signal analysis:

where R_B is the base bias resistance and r_π = β/g_m, with β being the current gain and g_m the transconductance. The parallel combination often results in moderate input impedance (typically 1–10 kΩ).

In contrast, a common-collector (emitter-follower) configuration offers higher input impedance due to series feedback introduced by the emitter resistor R_E:

This topology is favored for impedance matching in high-frequency or buffer applications.

Field-Effect Transistor (FET) Topologies

FET-based amplifiers, such as the common-source configuration, exhibit input impedance dominated by the gate biasing network, as the gate current is negligible:

where R_G is the gate resistor. This can reach megaohms, making FETs suitable for high-impedance sensor interfaces.

A common-drain (source-follower) topology, analogous to the BJT emitter-follower, provides:

where R_S is the source resistor. The term 1/g_m typically dominates, yielding lower impedance than common-source but higher than common-emitter.

Feedback and Cascading Effects

Global or local feedback networks further modulate input impedance. For instance, shunt feedback reduces input impedance, while series feedback increases it. In multistage amplifiers, the input impedance of subsequent stages loads the preceding one, necessitating careful design to avoid signal degradation.

Practical Implications

• Matching Networks: Impedance mismatches lead to reflections in RF systems, necessitating topologies like common-collector for minimal loss.
• Noise Performance: High input impedance reduces thermal noise but may increase susceptibility to capacitive coupling.
• Frequency Dependence: At high frequencies, parasitic capacitances (e.g., C_gs in FETs) shunt the input, lowering effective impedance.

The input impedance of an amplifier is not purely resistive and often exhibits frequency-dependent behavior due to reactive components such as parasitic capacitances and inductances. At low frequencies, the input impedance is dominated by the DC bias network and transistor parameters, while at high frequencies, parasitic effects and device capacitances become significant.

Small-Signal Model and Frequency Effects

In a bipolar junction transistor (BJT) or field-effect transistor (FET) amplifier, the input impedance can be modeled using a small-signal equivalent circuit. For a common-emitter BJT amplifier, the input impedance Z_in includes the base resistance r_π, the base-emitter capacitance C_π, and the Miller-effect multiplied capacitance C_μ:

where g_m is the transconductance, R_L is the load resistance, and ω is the angular frequency. The Miller effect increases the effective input capacitance, reducing impedance at higher frequencies.

High-Frequency Roll-off and Bandwidth Limitations

As frequency increases, the capacitive reactance decreases, causing the input impedance to drop. The frequency at which the impedance magnitude falls to 1/√2 of its low-frequency value defines the upper cutoff frequency f_H:

Here, R_B represents the biasing network resistance. Beyond f_H, the amplifier's gain decreases due to the increasing shunting effect of capacitance.

FET Amplifier Input Impedance

For a MOSFET common-source amplifier, the gate input impedance is primarily capacitive at high frequencies:

where C_gs is the gate-source capacitance, C_gd is the gate-drain capacitance, and R_D is the drain resistance. The Miller effect similarly enhances C_gd, reducing input impedance.

Practical Implications in Circuit Design

In RF and high-speed amplifiers, impedance matching is critical to minimize reflections and signal distortion. A mismatched input impedance can lead to:

• Signal attenuation due to reflection losses.
• Frequency-dependent gain variations, degrading amplifier linearity.
• Oscillations or instability in feedback configurations.

Techniques such as inductive peaking or cascode topologies can mitigate high-frequency impedance degradation by reducing the Miller effect and improving bandwidth.

Measurement and Simulation

Input impedance can be measured using a network analyzer or derived from S-parameters (S₁₁). In SPICE simulations, an AC analysis sweep reveals the frequency response of Z_in, helping designers optimize matching networks.

The input impedance of an amplifier is not purely resistive and often exhibits frequency-dependent behavior due to reactive components such as parasitic capacitances and inductances. At low frequencies, the input impedance is dominated by the DC bias network and transistor parameters, while at high frequencies, parasitic effects and device capacitances become significant.

Small-Signal Model and Frequency Effects

In a bipolar junction transistor (BJT) or field-effect transistor (FET) amplifier, the input impedance can be modeled using a small-signal equivalent circuit. For a common-emitter BJT amplifier, the input impedance Z_in includes the base resistance r_π, the base-emitter capacitance C_π, and the Miller-effect multiplied capacitance C_μ:

where g_m is the transconductance, R_L is the load resistance, and ω is the angular frequency. The Miller effect increases the effective input capacitance, reducing impedance at higher frequencies.

High-Frequency Roll-off and Bandwidth Limitations

As frequency increases, the capacitive reactance decreases, causing the input impedance to drop. The frequency at which the impedance magnitude falls to 1/√2 of its low-frequency value defines the upper cutoff frequency f_H:

Here, R_B represents the biasing network resistance. Beyond f_H, the amplifier's gain decreases due to the increasing shunting effect of capacitance.

FET Amplifier Input Impedance

For a MOSFET common-source amplifier, the gate input impedance is primarily capacitive at high frequencies:

where C_gs is the gate-source capacitance, C_gd is the gate-drain capacitance, and R_D is the drain resistance. The Miller effect similarly enhances C_gd, reducing input impedance.

Practical Implications in Circuit Design

In RF and high-speed amplifiers, impedance matching is critical to minimize reflections and signal distortion. A mismatched input impedance can lead to:

• Signal attenuation due to reflection losses.
• Frequency-dependent gain variations, degrading amplifier linearity.
• Oscillations or instability in feedback configurations.

Techniques such as inductive peaking or cascode topologies can mitigate high-frequency impedance degradation by reducing the Miller effect and improving bandwidth.

Measurement and Simulation

Input impedance can be measured using a network analyzer or derived from S-parameters (S₁₁). In SPICE simulations, an AC analysis sweep reveals the frequency response of Z_in, helping designers optimize matching networks.

Feedback fundamentally alters the input impedance of an amplifier, with the magnitude and direction of change determined by the feedback topology. The two primary feedback configurations—series feedback (voltage mixing) and shunt feedback (current mixing)—affect input impedance differently.

Series Feedback (Voltage Mixing)

In series feedback, the feedback signal is applied in series with the input voltage. This configuration increases the input impedance due to the voltage opposition effect. For a non-inverting amplifier with feedback factor β and open-loop gain A, the input impedance Z_in,fb is derived as follows:

where Z_in,0 is the open-loop input impedance. The term (1 + Aβ) represents the loop gain, which scales the impedance proportionally. This effect is exploited in high-input-impedance applications such as electrometer amplifiers and sensor interfaces.

Shunt Feedback (Current Mixing)

Shunt feedback, where the feedback current is summed at the input node, reduces the input impedance. For an inverting amplifier, the input impedance Z_in,fb is approximated by:

This reduction occurs because the feedback current effectively "shunts" the input, lowering the impedance seen by the source. Practical examples include transimpedance amplifiers (TIAs) in photodiode circuits, where low input impedance minimizes voltage noise.

Generalized Feedback Analysis

The exact input impedance modification depends on the amplifier's feedback network. Using Blackman's impedance formula, the closed-loop input impedance Z_in,fb can be expressed as:

where T_sc and T_oc are the loop gains under short-circuit and open-circuit conditions, respectively. This formulation is particularly useful in analyzing complex feedback networks, such as those found in multi-stage amplifiers.

Practical Implications

• Stability Considerations: High input impedance in series feedback can lead to increased susceptibility to stray capacitance, necessitating careful PCB layout.
• Noise Trade-offs: Shunt feedback’s lower input impedance reduces thermal noise but may increase current noise contribution from the feedback network.
• Frequency Dependence: The loop gain Aβ varies with frequency, causing input impedance to change across the amplifier’s bandwidth.

In RF amplifiers, for instance, the input impedance variation with frequency must be matched to the source impedance to prevent reflections and power loss. This is critical in applications like low-noise amplifiers (LNAs) for wireless receivers.

Feedback fundamentally alters the input impedance of an amplifier, with the magnitude and direction of change determined by the feedback topology. The two primary feedback configurations—series feedback (voltage mixing) and shunt feedback (current mixing)—affect input impedance differently.

Series Feedback (Voltage Mixing)

In series feedback, the feedback signal is applied in series with the input voltage. This configuration increases the input impedance due to the voltage opposition effect. For a non-inverting amplifier with feedback factor β and open-loop gain A, the input impedance Z_in,fb is derived as follows:

where Z_in,0 is the open-loop input impedance. The term (1 + Aβ) represents the loop gain, which scales the impedance proportionally. This effect is exploited in high-input-impedance applications such as electrometer amplifiers and sensor interfaces.

Shunt Feedback (Current Mixing)

Shunt feedback, where the feedback current is summed at the input node, reduces the input impedance. For an inverting amplifier, the input impedance Z_in,fb is approximated by:

This reduction occurs because the feedback current effectively "shunts" the input, lowering the impedance seen by the source. Practical examples include transimpedance amplifiers (TIAs) in photodiode circuits, where low input impedance minimizes voltage noise.

Generalized Feedback Analysis

The exact input impedance modification depends on the amplifier's feedback network. Using Blackman's impedance formula, the closed-loop input impedance Z_in,fb can be expressed as:

where T_sc and T_oc are the loop gains under short-circuit and open-circuit conditions, respectively. This formulation is particularly useful in analyzing complex feedback networks, such as those found in multi-stage amplifiers.

Practical Implications

• Stability Considerations: High input impedance in series feedback can lead to increased susceptibility to stray capacitance, necessitating careful PCB layout.
• Noise Trade-offs: Shunt feedback’s lower input impedance reduces thermal noise but may increase current noise contribution from the feedback network.
• Frequency Dependence: The loop gain Aβ varies with frequency, causing input impedance to change across the amplifier’s bandwidth.

In RF amplifiers, for instance, the input impedance variation with frequency must be matched to the source impedance to prevent reflections and power loss. This is critical in applications like low-noise amplifiers (LNAs) for wireless receivers.

The input impedance of a common-emitter (CE) amplifier is a critical parameter that determines how the amplifier interacts with the signal source. Unlike idealized models, real-world CE amplifiers exhibit input impedance influenced by both DC biasing conditions and small-signal AC behavior.

DC and AC Components

The total input impedance (Z_in) comprises two parallel contributions:

• DC bias resistance (R_B): Thevenin equivalent of the base biasing network.
• Small-signal input resistance (r_π): Dynamic resistance seen by the AC signal.

Derivation of r_π

The small-signal input resistance r_π is derived from the transistor's transconductance (g_m) and DC bias current (I_C):

where β is the current gain, V_T is the thermal voltage (~26 mV at 300 K), and I_C is the collector bias current.

Practical Considerations

In real circuits, the input impedance is further affected by:

• Emitter degeneration: Adding an emitter resistor R_E increases input impedance to approximately β(R_E + r_e), where r_e = V_T/I_C.
• Parasitic capacitances: At high frequencies, C_π and C_μ shunt the input, reducing impedance.

Measurement Techniques

Input impedance can be measured experimentally by:

• Voltage divider method: Insert a known series resistor and measure voltage attenuation.
• Network analyzer: Direct impedance measurement using S-parameters.

Design Implications

Mismatched input impedance causes:

• Signal reflection in RF applications, degrading power transfer.
• Loading effects in cascaded stages, altering frequency response.

where Z_s is the source impedance.

The input impedance of a common-emitter (CE) amplifier is a critical parameter that determines how the amplifier interacts with the signal source. Unlike idealized models, real-world CE amplifiers exhibit input impedance influenced by both DC biasing conditions and small-signal AC behavior.

DC and AC Components

The total input impedance (Z_in) comprises two parallel contributions:

• DC bias resistance (R_B): Thevenin equivalent of the base biasing network.
• Small-signal input resistance (r_π): Dynamic resistance seen by the AC signal.

Derivation of r_π

The small-signal input resistance r_π is derived from the transistor's transconductance (g_m) and DC bias current (I_C):

where β is the current gain, V_T is the thermal voltage (~26 mV at 300 K), and I_C is the collector bias current.

Practical Considerations

In real circuits, the input impedance is further affected by:

• Emitter degeneration: Adding an emitter resistor R_E increases input impedance to approximately β(R_E + r_e), where r_e = V_T/I_C.
• Parasitic capacitances: At high frequencies, C_π and C_μ shunt the input, reducing impedance.

Measurement Techniques

Input impedance can be measured experimentally by:

• Voltage divider method: Insert a known series resistor and measure voltage attenuation.
• Network analyzer: Direct impedance measurement using S-parameters.

Design Implications

Mismatched input impedance causes:

• Signal reflection in RF applications, degrading power transfer.
• Loading effects in cascaded stages, altering frequency response.

where Z_s is the source impedance.

The input impedance of a common-collector (CC) amplifier, also known as an emitter-follower, is significantly influenced by its high current gain and negative feedback mechanism. Unlike common-emitter configurations, the CC amplifier exhibits a relatively high input impedance due to the emitter resistor's feedback effect.

Derivation of Input Impedance

For a bipolar junction transistor (BJT) in a common-collector configuration, the small-signal input impedance (Z_in) can be derived by analyzing the hybrid-π model. The input impedance is primarily determined by the base-emitter resistance (r_π), the transconductance (g_m), and the emitter resistance (R_E).

where:

• r_π = small-signal base-emitter resistance,
• β = current gain (h_FE),
• R_E = emitter resistor,
• r_o = small-signal output resistance of the transistor.

Since β is typically large (50–300), the term (β + 1)(R_E || r_o) dominates, leading to a high input impedance. If R_E is bypassed with a capacitor, the impedance seen at the base reduces to r_π.

Effect of Load Resistance

When a load resistor (R_L) is connected to the emitter, the effective emitter resistance becomes R_E || R_L. This modifies the input impedance as:

This relationship highlights the dependence of Z_in on the external load, making the common-collector amplifier particularly useful for impedance matching in buffer applications.

Practical Implications

The high input impedance of the common-collector amplifier minimizes loading effects on preceding stages, making it ideal for voltage buffering. In RF and audio circuits, this property ensures efficient signal transfer between high-impedance sources and low-impedance loads.

For example, in a microphone preamplifier, a CC stage can prevent signal degradation by presenting a sufficiently high impedance to the transducer while driving a low-impedance transmission line.

Comparison with Other Configurations

• Common-Emitter (CE): Input impedance is primarily r_π, typically lower than CC.
• Common-Base (CB): Input impedance is very low (~1/g_m), unsuitable for high-impedance sources.

Thus, the common-collector topology is preferred when high input impedance is critical, such as in voltage followers or impedance transformation networks.

The input impedance of a common-collector (CC) amplifier, also known as an emitter-follower, is significantly influenced by its high current gain and negative feedback mechanism. Unlike common-emitter configurations, the CC amplifier exhibits a relatively high input impedance due to the emitter resistor's feedback effect.

Derivation of Input Impedance

For a bipolar junction transistor (BJT) in a common-collector configuration, the small-signal input impedance (Z_in) can be derived by analyzing the hybrid-π model. The input impedance is primarily determined by the base-emitter resistance (r_π), the transconductance (g_m), and the emitter resistance (R_E).

where:

• r_π = small-signal base-emitter resistance,
• β = current gain (h_FE),
• R_E = emitter resistor,
• r_o = small-signal output resistance of the transistor.

Since β is typically large (50–300), the term (β + 1)(R_E || r_o) dominates, leading to a high input impedance. If R_E is bypassed with a capacitor, the impedance seen at the base reduces to r_π.

Effect of Load Resistance

When a load resistor (R_L) is connected to the emitter, the effective emitter resistance becomes R_E || R_L. This modifies the input impedance as:

This relationship highlights the dependence of Z_in on the external load, making the common-collector amplifier particularly useful for impedance matching in buffer applications.

Practical Implications

The high input impedance of the common-collector amplifier minimizes loading effects on preceding stages, making it ideal for voltage buffering. In RF and audio circuits, this property ensures efficient signal transfer between high-impedance sources and low-impedance loads.

For example, in a microphone preamplifier, a CC stage can prevent signal degradation by presenting a sufficiently high impedance to the transducer while driving a low-impedance transmission line.

Comparison with Other Configurations

• Common-Emitter (CE): Input impedance is primarily r_π, typically lower than CC.
• Common-Base (CB): Input impedance is very low (~1/g_m), unsuitable for high-impedance sources.

Thus, the common-collector topology is preferred when high input impedance is critical, such as in voltage followers or impedance transformation networks.

The input impedance of an operational amplifier (op-amp) is a critical parameter that determines how the amplifier interacts with the source signal. Unlike discrete transistor amplifiers, op-amps are designed with extremely high input impedance to minimize loading effects on the input source. This property arises from their differential input stage, typically implemented using a pair of bipolar junction transistors (BJTs) or field-effect transistors (FETs).

Ideal vs. Real Input Impedance

An ideal op-amp has infinite input impedance, meaning it draws zero current from the input source. However, real op-amps exhibit finite input impedance due to:

• Differential input resistance (R_id) – The impedance between the non-inverting and inverting inputs.
• Common-mode input resistance (R_icm) – The impedance from each input to ground.

For a BJT-based op-amp like the LM741, R_id is typically in the range of 2 MΩ, while FET-based op-amps (e.g., TL081) can exceed 10¹² Ω.

Mathematical Derivation

The input impedance (Z_in) of an op-amp circuit depends on the feedback configuration. For a non-inverting amplifier:

where:

• A_OL is the open-loop gain,
• β is the feedback factor (R₁/(R₁ + R₂)),
• Z_in(OL) is the open-loop input impedance.

In a voltage follower configuration (unity gain), this simplifies to:

Practical Implications

High input impedance is crucial in applications such as:

• Sensor interfaces – Prevents signal attenuation from high-impedance sources (e.g., piezoelectric sensors).
• Medical instrumentation – Ensures minimal current draw from biological tissues.
• Active filters – Maintains desired frequency response without loading preceding stages.

Frequency Dependence

Input impedance decreases at higher frequencies due to:

• Parasitic capacitances (C_in) across input terminals.
• The diminishing open-loop gain (A_OL) with frequency.

The capacitive reactance component becomes dominant, given by:

where f is the frequency. This roll-off must be accounted for in high-speed or RF applications.

Measurement Techniques

Input impedance can be measured experimentally by:

• Voltage divider method – Inserting a known series resistor and measuring attenuation.
• Impedance analyzer – Direct measurement using network analysis tools.

The input impedance of an operational amplifier (op-amp) is a critical parameter that determines how the amplifier interacts with the source signal. Unlike discrete transistor amplifiers, op-amps are designed with extremely high input impedance to minimize loading effects on the input source. This property arises from their differential input stage, typically implemented using a pair of bipolar junction transistors (BJTs) or field-effect transistors (FETs).

Ideal vs. Real Input Impedance

An ideal op-amp has infinite input impedance, meaning it draws zero current from the input source. However, real op-amps exhibit finite input impedance due to:

• Differential input resistance (R_id) – The impedance between the non-inverting and inverting inputs.
• Common-mode input resistance (R_icm) – The impedance from each input to ground.

For a BJT-based op-amp like the LM741, R_id is typically in the range of 2 MΩ, while FET-based op-amps (e.g., TL081) can exceed 10¹² Ω.

Mathematical Derivation

The input impedance (Z_in) of an op-amp circuit depends on the feedback configuration. For a non-inverting amplifier:

where:

• A_OL is the open-loop gain,
• β is the feedback factor (R₁/(R₁ + R₂)),
• Z_in(OL) is the open-loop input impedance.

In a voltage follower configuration (unity gain), this simplifies to:

Practical Implications

High input impedance is crucial in applications such as:

• Sensor interfaces – Prevents signal attenuation from high-impedance sources (e.g., piezoelectric sensors).
• Medical instrumentation – Ensures minimal current draw from biological tissues.
• Active filters – Maintains desired frequency response without loading preceding stages.

Frequency Dependence

Input impedance decreases at higher frequencies due to:

• Parasitic capacitances (C_in) across input terminals.
• The diminishing open-loop gain (A_OL) with frequency.

The capacitive reactance component becomes dominant, given by:

where f is the frequency. This roll-off must be accounted for in high-speed or RF applications.

Measurement Techniques

Input impedance can be measured experimentally by:

• Voltage divider method – Inserting a known series resistor and measuring attenuation.
• Impedance analyzer – Direct measurement using network analysis tools.

• Input and Output Impedances of Amplifiers - Electronics-Lab.com — In more technical terms, the flow of current of both the input and output is controlled by the input and output impedance of the amplifier. This tutorial clarifies the notions of input and output amplifiers impedances by explaining the previously mentioned concept of "box".
• Input-Output Impedance of Amplifiers | SpringerLink — In the previous chapter you learned how to draw the frequency response of different types of amplifiers. In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero.
• PDF Power Amplifiers - Learn About Electronics — Amplifier circuits form the basis of most electronic systems, many of which need to produce high power to drive some output device. Audio amplifier output power may be anything from less than 1 Watt to several hundred Watts. Radio frequency amplifiers used in transmitters can be required to produce thousands of kilowatts of output power, and DC amplifiers used in electronic control systems may ...
• PDF Designing Audio Power Amplifiers - pearl-hifi.com — The input impedance of real loudspeakers can vary dramatically as a function of fre-quency, while the output impedance of the power amplifier is nonzero. A voltage divider is thus formed by the amplifier output impedance and the loudspeaker input impedance, as illustrated in Figure 1.4.
• PDF Alexander - Fundamentals of Electric Circuits 3e HQ — Thus, an ideal op amp has zero current into its two input terminals and negligibly small voltage between the two input terminals. Equations (5.5) and (5.7) are extremely important and should be regarded as the key handles to analyzing op amp circuits.
• Input-Output Impedance of Amplifiers - Springer — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimu- lating source. The output impedance is the impedance seen from the output when stimulating source is zero.
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, Vs and Rs, and output load, RL. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit.
• PDF LiU-TEK-LIC-2009_1414 - DiVA — To achieve a complete model and to accurately predict power gain, input and output impedance, and phase delay between the current and the gate voltage, a number of resistive components should also be included at the drain, source, gate, and substrate.
• (PDF) Chapter 5 Operational Amplifiers - Academia.edu — The op amp is a high-gain amplifier that has high input resistance and low output resistance. | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents fCHAPTER 5 Operational Amplifiers 2.
• PDF Op Amps for Everyone Design Guide (Rev - MIT — Then some of the amplifier output signal was fed back to the input in a manner that makes the circuit gain (circuit is the amplifier and feedback components) dependent on the feedback circuit rather than the amplifier gain.

• Input and Output Impedances of Amplifiers - Electronics-Lab.com — In more technical terms, the flow of current of both the input and output is controlled by the input and output impedance of the amplifier. This tutorial clarifies the notions of input and output amplifiers impedances by explaining the previously mentioned concept of "box".
• Input-Output Impedance of Amplifiers | SpringerLink — In the previous chapter you learned how to draw the frequency response of different types of amplifiers. In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero.
• PDF Power Amplifiers - Learn About Electronics — Amplifier circuits form the basis of most electronic systems, many of which need to produce high power to drive some output device. Audio amplifier output power may be anything from less than 1 Watt to several hundred Watts. Radio frequency amplifiers used in transmitters can be required to produce thousands of kilowatts of output power, and DC amplifiers used in electronic control systems may ...
• PDF Designing Audio Power Amplifiers - pearl-hifi.com — The input impedance of real loudspeakers can vary dramatically as a function of fre-quency, while the output impedance of the power amplifier is nonzero. A voltage divider is thus formed by the amplifier output impedance and the loudspeaker input impedance, as illustrated in Figure 1.4.
• PDF Alexander - Fundamentals of Electric Circuits 3e HQ — Thus, an ideal op amp has zero current into its two input terminals and negligibly small voltage between the two input terminals. Equations (5.5) and (5.7) are extremely important and should be regarded as the key handles to analyzing op amp circuits.
• Input-Output Impedance of Amplifiers - Springer — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimu- lating source. The output impedance is the impedance seen from the output when stimulating source is zero.
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, Vs and Rs, and output load, RL. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit.
• PDF LiU-TEK-LIC-2009_1414 - DiVA — To achieve a complete model and to accurately predict power gain, input and output impedance, and phase delay between the current and the gate voltage, a number of resistive components should also be included at the drain, source, gate, and substrate.
• (PDF) Chapter 5 Operational Amplifiers - Academia.edu — The op amp is a high-gain amplifier that has high input resistance and low output resistance. | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents fCHAPTER 5 Operational Amplifiers 2.
• PDF Op Amps for Everyone Design Guide (Rev - MIT — Then some of the amplifier output signal was fed back to the input in a manner that makes the circuit gain (circuit is the amplifier and feedback components) dependent on the feedback circuit rather than the amplifier gain.

• PDF Lecture Notes for Analog Electronics - University of Oregon — 1.5.2 Input and Output Impedance Oursimple example can also beused toillustrate theimportant concepts ofinput and output resistance. (Shortly, we will generalize our discussion and substitute the term \impedance" for resistance. We can get a head start by using the common terms \input impedance" and \output impedance" at this point.)
• Unit 5: Amplifier Concepts - Semiconductor Devices: Theory and ... - NSCC — Determine the effects of source and load impedance on system gain and explain how they interact with an amplifier's input and output impedance. Describe and distinguish the concepts of noise and waveform distortion. Define the concept of output compliance. Discuss the frequency limits of an amplifier in general terms. Define Miller's Theorem.
• Input-Output Impedance of Amplifiers - Springer — 136 5 Input-Output Impedance of Amplifiers. 5.2 Input Impedance of Inverting Amplifier . In this section we want to draw the input impedance of the inverting amplifier shown in Fig. 5.1. Draw the schematic shown in Fig. 5.1. Fig. 5.1 . Sample inverting amplifier
• Input-Output Impedance of Amplifiers - SpringerLink — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero. ... Asadi F., Eguchi K., Electronic Measurement: A Practical Approach, Springer, 2021. DOI: https ...
• PDF Fundamentals of Microelectronics - The University of Texas at Dallas — In this example, the input impedance of Q 2 can be combined in parallel with R C to yield an equivalent collector impedance to ground. E m C v R g R r A + = − 1 2 1 || π CH5 Bipolar Amplifiers 40 Input Impedance of Degenerated CE Stage With emitter degeneration, the input impedance is increased from r ππππ to rππππ + (ββββ+1)R E ...
• Class AB Amplifier - Basic Electronics Tutorials and Revision — Class A: - The amplifiers single output transistor conducts for the full 360 o of the cycle of the input waveform. Class B: - The amplifiers two output transistors only conduct for one-half, that is, 180 o of the input waveform. Class AB: - The amplifiers two output transistors conduct somewhere between 180 o and 360 o of the input waveform.
• PDF ECE 3274 Two-Stage Amplifier Project 1. Objective - Virginia Tech — The CS-CC cascade two-stage amplifier is a good multistage configuration because the CS and CC amplifiers together provide some very desirable characteristics. The CS amplifier makes up the first stage and is capable of providing high voltage gain. The input impedance of the CS is a function of Rg1 and Rg2 and is generally very high.
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, V. s . and R. s, and output load, R. L. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit. R. S + R. I. R. O + AVi R. L. Inp ut Port + Opu utt Port + ± ± V V. I. V. L S. Source Ampliifer Load. Figure 1-1. Thevenin Model of Amplifier ...
• 5.2 Amplifier Model - Semiconductor Devices: Theory and Application — A voltage amplifier has the following specifications: A v = 20 , Z in = 10 kΩ, Z out = 200Ω. It is driven by a 30 millivolt source with a 600 Ω internal impedance and drives a 1 kΩ load. Determine the load voltage. The voltage that appears at the amplifier's input is
• PDF OPERATIONAL AMPLIFIERS: Basic Circuits and Applications - Texas A&M ... — •Op Amp is a voltage amplifier with extremely high gain (741, Gain: 200,000 (V/V), Op-77, Gain: 12 (V/uV ) • r d, a, r o are open-loop parameters • v P: Non-inverting v N: Inverting • v 0 = a. v D = a (v P -v N) The Ideal Op Amp: •The virtual input short does not draw any current •For voltage purposes: Input appears as a short circuit

• PDF Lecture Notes for Analog Electronics - University of Oregon — 1.5.2 Input and Output Impedance Oursimple example can also beused toillustrate theimportant concepts ofinput and output resistance. (Shortly, we will generalize our discussion and substitute the term \impedance" for resistance. We can get a head start by using the common terms \input impedance" and \output impedance" at this point.)
• Unit 5: Amplifier Concepts - Semiconductor Devices: Theory and ... - NSCC — Determine the effects of source and load impedance on system gain and explain how they interact with an amplifier's input and output impedance. Describe and distinguish the concepts of noise and waveform distortion. Define the concept of output compliance. Discuss the frequency limits of an amplifier in general terms. Define Miller's Theorem.
• Input-Output Impedance of Amplifiers - Springer — 136 5 Input-Output Impedance of Amplifiers. 5.2 Input Impedance of Inverting Amplifier . In this section we want to draw the input impedance of the inverting amplifier shown in Fig. 5.1. Draw the schematic shown in Fig. 5.1. Fig. 5.1 . Sample inverting amplifier
• Input-Output Impedance of Amplifiers - SpringerLink — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero. ... Asadi F., Eguchi K., Electronic Measurement: A Practical Approach, Springer, 2021. DOI: https ...
• PDF Fundamentals of Microelectronics - The University of Texas at Dallas — In this example, the input impedance of Q 2 can be combined in parallel with R C to yield an equivalent collector impedance to ground. E m C v R g R r A + = − 1 2 1 || π CH5 Bipolar Amplifiers 40 Input Impedance of Degenerated CE Stage With emitter degeneration, the input impedance is increased from r ππππ to rππππ + (ββββ+1)R E ...
• Class AB Amplifier - Basic Electronics Tutorials and Revision — Class A: - The amplifiers single output transistor conducts for the full 360 o of the cycle of the input waveform. Class B: - The amplifiers two output transistors only conduct for one-half, that is, 180 o of the input waveform. Class AB: - The amplifiers two output transistors conduct somewhere between 180 o and 360 o of the input waveform.
• PDF ECE 3274 Two-Stage Amplifier Project 1. Objective - Virginia Tech — The CS-CC cascade two-stage amplifier is a good multistage configuration because the CS and CC amplifiers together provide some very desirable characteristics. The CS amplifier makes up the first stage and is capable of providing high voltage gain. The input impedance of the CS is a function of Rg1 and Rg2 and is generally very high.
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, V. s . and R. s, and output load, R. L. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit. R. S + R. I. R. O + AVi R. L. Inp ut Port + Opu utt Port + ± ± V V. I. V. L S. Source Ampliifer Load. Figure 1-1. Thevenin Model of Amplifier ...
• 5.2 Amplifier Model - Semiconductor Devices: Theory and Application — A voltage amplifier has the following specifications: A v = 20 , Z in = 10 kΩ, Z out = 200Ω. It is driven by a 30 millivolt source with a 600 Ω internal impedance and drives a 1 kΩ load. Determine the load voltage. The voltage that appears at the amplifier's input is
• PDF OPERATIONAL AMPLIFIERS: Basic Circuits and Applications - Texas A&M ... — •Op Amp is a voltage amplifier with extremely high gain (741, Gain: 200,000 (V/V), Op-77, Gain: 12 (V/uV ) • r d, a, r o are open-loop parameters • v P: Non-inverting v N: Inverting • v 0 = a. v D = a (v P -v N) The Ideal Op Amp: •The virtual input short does not draw any current •For voltage purposes: Input appears as a short circuit

• Input Impedance - an overview | ScienceDirect Topics — Input Impedance. The input impedance for the AC-coupled inverting amplifier circuit shown in Figure 2.27(a) is equal to the net impedance of R I and C I.Recall that the (−) input of the op amp is a virtual ground point. The source, therefore, sees the input impedance offered by C I and R I.Because this is a frequency-dependent value, we must discuss input impedance at a particular frequency ...
• Input-Output Impedance of Amplifiers - SpringerLink — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero. ... References for Further Study. Sedra A., Smith K., Microelectronics Circuits, Oxford University ...
• PDF OPERATIONAL AMPLIFIERS: Theory and Practice - MIT OpenCourseWare — Some of the more advanced applications in Chapters 11 and 12 have been included in a graduate course in analog and analog/digital instru- ... 2.5 Effects of Feedback on Input and Output Impedance 46 Problems 54 xi. xii Contents Page III LINEAR SYSTEM RESPONSE 63 ... 7.2 Drift Referred to the Input 250 7.3 The Differential Amplifier 254 7.3.1 ...
• PDF Fundamentals of Microelectronics - The University of Texas at Dallas — In this example, the input impedance of Q 2 can be combined in parallel with R C to yield an equivalent collector impedance to ground. E m C v R g R r A + = − 1 2 1 || π CH5 Bipolar Amplifiers 40 Input Impedance of Degenerated CE Stage With emitter degeneration, the input impedance is increased from r ππππ to rππππ + (ββββ+1)R E ...
• PDF Understanding Basic Analog Ideal Op Amps (Rev. B) - Texas Instruments — ground, then the other input is at the same potential. The current flow into the input leads is zero, so the input impedance of the op amp is infinite. Four, the output impedance of the ideal op amp is zero. The ideal op amp can drive any load without an output impedance dropping voltage across it. The output impedance of most op amps
• 5.3: Common Emitter Amplifier - Engineering LibreTexts — Electronics (Final) 5: Lab Exercises ... The objective of this exercise is to examine the characteristics of a common emitter amplifier, specifically voltage gain, input impedance and output impedance. A method for experimentally determining input and output impedance is investigated along with various potential troubleshooting issues.
• 2.5: Effects of Feedback on Input and Output Impedance — Thus the current required from the input-signal source will be small, implying high input impedance. The topology shown in Figure 2.16\(b\) reduces input impedance, since only a small voltage appears across the parallel input-signal and amplifier-input connection. Figure 2.16 Two possible input topologies. (\(a\)) Input signal applied in series ...
• PDF Part IV Lectures 19 & 20 Multistage and Feedback Amplifiers — The input impedance of the amplifier is that of . stage. 1, i G = = 3..3 Z R M Ω . While the output impedance of the amplifier is that of stage2, o C = = 2.2. Z R k Ω. If a 10-kΩ load is connected to the output, the resulting voltage across the load is: V k k k R Z R V V L o L o L 0.49 10 2.2 (10 )(0.6) = + = + ⋅ =. Frequency Response of ...
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, V. s . and R. s, and output load, R. L. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit. R. S + R. I. R. O + AVi R. L. Inp ut Port + Opu utt Port + ± ± V V. I. V. L S. Source Ampliifer Load. Figure 1-1. Thevenin Model of Amplifier ...
• Chapter 16: Advanced Amplifier topics: - Analog — As illustrated, the input is 10 KHz and the output is 20 KHz, or twice the input frequency. In other words, the second harmonic of 10 KHz is 20 KHz. The third harmonic (frequency tripler) would be 30 KHz, or 3 times the input signal. The fourth harmonic (quadruplet) would be 40 KHz, or 4 times the 10 KHz input signal.

• Input Impedance - an overview | ScienceDirect Topics — Input Impedance. The input impedance for the AC-coupled inverting amplifier circuit shown in Figure 2.27(a) is equal to the net impedance of R I and C I.Recall that the (−) input of the op amp is a virtual ground point. The source, therefore, sees the input impedance offered by C I and R I.Because this is a frequency-dependent value, we must discuss input impedance at a particular frequency ...
• Input-Output Impedance of Amplifiers - SpringerLink — In this chapter you will learn how to draw the input or output impedance of an amplifier. The input impedance is the impedance seen by stimulating source. The output impedance is the impedance seen from the output when stimulating source is zero. ... References for Further Study. Sedra A., Smith K., Microelectronics Circuits, Oxford University ...
• PDF OPERATIONAL AMPLIFIERS: Theory and Practice - MIT OpenCourseWare — Some of the more advanced applications in Chapters 11 and 12 have been included in a graduate course in analog and analog/digital instru- ... 2.5 Effects of Feedback on Input and Output Impedance 46 Problems 54 xi. xii Contents Page III LINEAR SYSTEM RESPONSE 63 ... 7.2 Drift Referred to the Input 250 7.3 The Differential Amplifier 254 7.3.1 ...
• PDF Fundamentals of Microelectronics - The University of Texas at Dallas — In this example, the input impedance of Q 2 can be combined in parallel with R C to yield an equivalent collector impedance to ground. E m C v R g R r A + = − 1 2 1 || π CH5 Bipolar Amplifiers 40 Input Impedance of Degenerated CE Stage With emitter degeneration, the input impedance is increased from r ππππ to rππππ + (ββββ+1)R E ...
• PDF Understanding Basic Analog Ideal Op Amps (Rev. B) - Texas Instruments — ground, then the other input is at the same potential. The current flow into the input leads is zero, so the input impedance of the op amp is infinite. Four, the output impedance of the ideal op amp is zero. The ideal op amp can drive any load without an output impedance dropping voltage across it. The output impedance of most op amps
• 5.3: Common Emitter Amplifier - Engineering LibreTexts — Electronics (Final) 5: Lab Exercises ... The objective of this exercise is to examine the characteristics of a common emitter amplifier, specifically voltage gain, input impedance and output impedance. A method for experimentally determining input and output impedance is investigated along with various potential troubleshooting issues.
• 2.5: Effects of Feedback on Input and Output Impedance — Thus the current required from the input-signal source will be small, implying high input impedance. The topology shown in Figure 2.16\(b\) reduces input impedance, since only a small voltage appears across the parallel input-signal and amplifier-input connection. Figure 2.16 Two possible input topologies. (\(a\)) Input signal applied in series ...
• PDF Part IV Lectures 19 & 20 Multistage and Feedback Amplifiers — The input impedance of the amplifier is that of . stage. 1, i G = = 3..3 Z R M Ω . While the output impedance of the amplifier is that of stage2, o C = = 2.2. Z R k Ω. If a 10-kΩ load is connected to the output, the resulting voltage across the load is: V k k k R Z R V V L o L o L 0.49 10 2.2 (10 )(0.6) = + = + ⋅ =. Frequency Response of ...
• Understanding Operational Amplifier Specifications (Rev. B) — To complete a simple amplifier circuit, we will include an input source and impedance, V. s . and R. s, and output load, R. L. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit. R. S + R. I. R. O + AVi R. L. Inp ut Port + Opu utt Port + ± ± V V. I. V. L S. Source Ampliifer Load. Figure 1-1. Thevenin Model of Amplifier ...
• Chapter 16: Advanced Amplifier topics: - Analog — As illustrated, the input is 10 KHz and the output is 20 KHz, or twice the input frequency. In other words, the second harmonic of 10 KHz is 20 KHz. The third harmonic (frequency tripler) would be 30 KHz, or 3 times the input signal. The fourth harmonic (quadruplet) would be 40 KHz, or 4 times the 10 KHz input signal.