Understanding Input Impedance and Output Impedance

 

Introduction

In the realm of electrical engineering and electronic circuit design, few concepts are as fundamental yet often misunderstood as input impedance and output impedance. These parameters play crucial roles in signal transmission, power transfer, and overall system performance. Whether you're designing audio equipment, RF systems, or digital circuits, a thorough understanding of impedance characteristics is essential for achieving optimal performance and preventing signal degradation.

Impedance, measured in ohms (Ω), represents the opposition to current flow in an AC circuit. Unlike simple resistance, impedance accounts for both resistive and reactive components, making it a complex quantity that varies with frequency. Input impedance refers to the impedance presented by a circuit or device at its input terminals, while output impedance represents the internal impedance of a source as seen from its output terminals.

This comprehensive guide will explore the fundamental principles of input and output impedance, their practical applications, measurement techniques, and the critical role they play in impedance matching for maximum power transfer and signal integrity.

Fundamental Concepts of Impedance

What is Impedance?

Impedance is the total opposition to alternating current flow in a circuit, combining both resistance (R) and reactance (X). It is expressed as a complex number:

Z = R + jX

Where:

• Z is the impedance
• R is the resistance component
• X is the reactance component
• j is the imaginary unit

The magnitude of impedance is calculated as: |Z| = √(R² + X²)

The phase angle is given by: θ = arctan(X/R)

Types of Reactive Components

Reactance can be either inductive or capacitive:

1. Inductive Reactance (XL): XL = 2πfL
   • Where f is frequency and L is inductance
   • Increases with frequency
   • Causes current to lag voltage by 90°
2. Capacitive Reactance (XC): XC = 1/(2πfC)
   • Where f is frequency and C is capacitance
   • Decreases with frequency
   • Causes current to lead voltage by 90°

Impedance vs. Resistance

Parameter
Resistance
Impedance
Circuit Type
DC and AC
AC only
Frequency Dependence
None
Yes
Mathematical Representation
Real number
Complex number
Components
Resistive only
Resistive + Reactive
Phase Shift
None
Possible
Unit
Ohms (Ω)
Ohms (Ω)

Input Impedance Fundamentals

Definition and Characteristics

Input impedance (Zin) is the impedance presented by a circuit, device, or system when viewed from its input terminals. It represents how much the input "loads" the driving source and affects signal transfer characteristics. Input impedance is frequency-dependent and can vary significantly across the operating bandwidth of a device.

Factors Affecting Input Impedance

Several factors influence the input impedance of electronic circuits:

1. Circuit Topology: The arrangement of components (series, parallel, or complex networks)
2. Component Values: Resistor, capacitor, and inductor values
3. Frequency: AC analysis shows impedance varies with frequency
4. Biasing Conditions: Operating point affects transistor parameters
5. Load Conditions: Output loading can affect input characteristics through feedback

Common Input Impedance Values

Different types of electronic devices exhibit characteristic input impedance ranges:

Device Type
Typical Input Impedance
Applications
Microphones (Dynamic)
150-600 Ω
Audio recording
Microphones (Condenser)
1-10 kΩ
Studio recording
Guitar Pickups
5-25 kΩ
Musical instruments
Op-Amp Inputs
1 MΩ - 1 TΩ
Signal processing
MOSFET Gates
> 1 GΩ
Digital circuits
Coaxial Cables
50 Ω or 75 Ω
RF/Video transmission
Audio Line Inputs
10-100 kΩ
Professional audio

Input Impedance in Different Circuit Configurations

Common Emitter Amplifier

For a bipolar junction transistor in common emitter configuration:

Zin ≈ β × re

Where β is the current gain and re is the emitter resistance.

Common Collector (Emitter Follower)

Zin ≈ β × (RE + re)

Where RE is the emitter resistance.

Operational Amplifier Circuits

For an ideal op-amp:

• Non-inverting input: Zin → ∞
• Inverting amplifier: Zin = R1 (feedback resistor)
• Non-inverting amplifier: Zin → ∞ (limited by op-amp specifications)

Output Impedance Fundamentals

Definition and Significance

Output impedance (Zout) represents the internal impedance of a source as seen looking back into its output terminals. It determines how much the source voltage will change under different load conditions and affects power transfer efficiency. A voltage source ideally has zero output impedance, while a current source ideally has infinite output impedance.

Thévenin and Norton Equivalent Circuits

Any linear circuit can be represented by its Thévenin or Norton equivalent:

Thévenin Equivalent:

• Voltage source (Vth) in series with output impedance (Zth)
• Zout = Zth

Norton Equivalent:

• Current source (In) in parallel with output impedance (Zn)
• Zout = Zn

Output Impedance Characteristics by Device Type

Device Type
Typical Output Impedance
Characteristics
Voltage Source
0 Ω (ideal)
Maintains constant voltage
Current Source
∞ Ω (ideal)
Maintains constant current
Audio Power Amplifier
0.1-8 Ω
Low for damping control
Tube Amplifiers
1-8 Ω
Higher than solid-state
Op-Amp Output
50-100 Ω
Varies with frequency
Function Generators
50 Ω
Matched to transmission lines
Battery
0.1-10 Ω
Increases with age/discharge

Effects of Output Impedance on Circuit Performance

Voltage Division

When a source with output impedance Zout drives a load ZL, voltage division occurs:

VL = Vsource × ZL/(Zout + ZL)

Frequency Response

Output impedance often varies with frequency, affecting:

• High-frequency rolloff due to parasitic capacitances
• Low-frequency rolloff due to coupling capacitors
• Resonant effects from inductances and capacitances

Impedance Matching Principles

Maximum Power Transfer Theorem

Maximum power transfer occurs when the load impedance equals the complex conjugate of the source impedance:

ZL = Zs*

For purely resistive circuits: RL = Rs

Power Transfer Efficiency

The efficiency of power transfer is given by:

η = RL/(Rs + RL)

Rs/RL Ratio
Efficiency
Power Transfer
1:1
50%
Maximum
1:2
66.7%
High
1:4
80%
Good
1:10
90.9%
Excellent

Voltage Transfer vs. Power Transfer

Different applications require different impedance relationships:

Voltage Transfer (High Efficiency):

• ZL >> Zs (typically 10:1 or greater)
• Maximizes voltage transfer
• Common in amplifier cascading

Power Transfer (Maximum Power):

• ZL = Zs
• 50% efficiency but maximum power
• Used in RF systems and audio power matching

Practical Applications and Design Considerations

Audio Systems

Microphone Preamp Design

Microphone preamps must present appropriate input impedance:

• Dynamic mics: 1-10 kΩ input impedance optimal
• Condenser mics: High impedance (>10 kΩ) to avoid loading
• Ribbon mics: Very high impedance (>50 kΩ) due to low output

Speaker Impedance Matching

Amplifier Output
Speaker Load
Result
8 Ω
8 Ω
Optimal power transfer
8 Ω
4 Ω
Higher current, possible overheating
8 Ω
16 Ω
Reduced power output
4 Ω
8 Ω
Reduced power, safe operation

RF and Microwave Systems

Transmission Line Matching

Standard impedance values:

• 50 Ω: Common for RF systems, measurement equipment
• 75 Ω: Video, cable TV, some antenna systems
• 300 Ω: Balanced antenna feedlines
• 600 Ω: Professional audio, telephony

Reflection Coefficient

The reflection coefficient (Γ) indicates impedance mismatch:

Γ = (ZL - Z0)/(ZL + Z0)

Where Z0 is the characteristic impedance of the transmission line.

Digital Circuit Considerations

High-Speed Digital Design

In high-speed digital circuits, impedance matching prevents:

• Signal reflections
• Overshoot and undershoot
• EMI radiation
• Crosstalk

PCB Trace Impedance

Controlled impedance traces require careful design:

• Single-ended: 50 Ω typical
• Differential pairs: 90-100 Ω typical
• Factors: trace width, thickness, dielectric constant, spacing

Measurement Techniques and Instrumentation

Input Impedance Measurement Methods

AC Voltage Division Method

1. Connect known resistor in series with unknown input impedance
2. Apply AC voltage and measure voltages across both
3. Calculate: Zin = R × (V2/V1)

Bridge Methods

AC Bridges:

• Maxwell bridge for inductive impedance
• Wien bridge for capacitive impedance
• Provides high accuracy for specific frequency ranges

Vector Network Analyzer (VNA)

Professional impedance measurement:

• Frequency range: DC to 100+ GHz
• Measures magnitude and phase
• Provides Smith chart displays
• High accuracy and repeatability

Output Impedance Measurement Techniques

Load Variation Method

1. Measure open-circuit voltage (Voc)
2. Connect known load and measure loaded voltage (VL)
3. Calculate: Zout = RL × (Voc - VL)/VL

Null Method

Using a bridge configuration to null the output, providing high accuracy for specific impedance values.

Modern Test Equipment

Instrument Type
Frequency Range
Impedance Range
Applications
LCR Meter
20 Hz - 300 MHz
mΩ to TΩ
Component testing
Vector Network Analyzer
10 MHz - 110 GHz
1 mΩ to 100 kΩ
RF/microwave
Impedance Analyzer
5 Hz - 120 MHz
μΩ to 100 MΩ
Material analysis
Time Domain Reflectometer
DC - 50 GHz
1 Ω - 1 kΩ
Cable testing

Advanced Topics and Special Cases

Frequency-Dependent Impedance

Miller Effect

In amplifier circuits, the Miller effect multiplies input capacitance:

Cin(Miller) = Cgd × (1 + Av)

Where Cgd is gate-drain capacitance and Av is voltage gain.

Parasitic Effects

At high frequencies, parasitic elements dominate:

• Lead inductance: L ≈ 1 nH/mm
• Package capacitance: typically 0.1-1 pF
• Bond wire inductance: 1-10 nH

Non-Linear Impedance Effects

Large Signal Behavior

Impedance can vary with signal amplitude due to:

• Transistor parameter variation
• Saturation effects
• Temperature dependencies

Intermodulation Distortion

Non-linear impedance creates harmonic content and intermodulation products, critical in RF design.

Temperature and Environmental Effects

Temperature Coefficients

Component
Typical Temp Coefficient
Carbon Resistors
+350 to -800 ppm/°C
Metal Film Resistors
±25 to ±100 ppm/°C
Ceramic Capacitors
-750 to +150 ppm/°C
Electrolytic Capacitors
-2% to +5% per °C

Humidity Effects

Particularly important for:

• High impedance circuits (>1 MΩ)
• PCB leakage currents
• Connector reliability

Troubleshooting Impedance-Related Issues

Common Problems and Solutions

Signal Distortion

Symptoms: Waveform distortion, frequency response changes Causes: Impedance mismatch, loading effects Solutions:

• Check impedance compatibility
• Use buffer amplifiers
• Implement proper termination

Oscillation

Symptoms: Unwanted oscillations, instability Causes: Feedback through impedance paths Solutions:

• Add damping resistors
• Improve grounding
• Use shielding

Power Transfer Issues

Symptoms: Reduced output power, heating Causes: Impedance mismatch between source and load Solutions:

• Use impedance matching networks
• Select appropriate component values
• Consider transformer coupling

Diagnostic Techniques

Smith Chart Analysis

The Smith Chart provides visual impedance analysis:

• Plots impedance and admittance
• Shows reflection coefficient relationships
• Aids in matching network design

S-Parameter Measurements

S-parameters describe impedance relationships in multi-port networks:

• S11: Input reflection coefficient
• S22: Output reflection coefficient
• S21: Forward transmission coefficient
• S12: Reverse transmission coefficient

Design Guidelines and Best Practices

Input Stage Design

High Input Impedance Circuits

For maximum voltage transfer:

• Use FET input stages
• Minimize input capacitance
• Provide high bias resistances
• Consider bootstrapping techniques

Low Noise Design

Optimize source impedance for minimum noise:

• Match source resistance to amplifier noise resistance
• Use low-noise transistors
• Minimize bandwidth where possible

Output Stage Design

Low Output Impedance

For voltage sources:

• Use emitter followers or source followers
• Implement negative feedback
• Use push-pull configurations
• Minimize series resistance

Current Source Applications

For high output impedance:

• Use cascode configurations
• Employ current mirrors
• Minimize shunt capacitances

PCB Layout Considerations

Trace Impedance Control

Parameter
50Ω Single-Ended
100Ω Differential
Trace Width (mil)
5.0
4.5
Trace Spacing (mil)
-
5.4
Dielectric Thickness (mil)
4.2
4.2
Er (dielectric constant)
4.3
4.3

Ground Plane Effects

• Solid ground planes reduce impedance variations
• Via stitching maintains ground continuity
• Guard rings isolate sensitive circuits

FAQ Section

1. What happens if input impedance is too low?

When input impedance is too low, it creates excessive loading on the driving source. This results in:

• Reduced signal amplitude due to voltage division
• Increased current draw from the source
• Potential distortion if the source cannot provide adequate current
• Reduced input voltage and possible source overheating

For example, if a 600Ω source drives a 150Ω input, only 20% of the source voltage appears at the input due to voltage division effects.

2. How does output impedance affect frequency response?

Output impedance significantly impacts frequency response through several mechanisms:

• High-frequency rolloff: Parasitic capacitances combine with output impedance to create low-pass filtering
• Low-frequency rolloff: Coupling capacitors and output impedance form high-pass filtering
• Resonant peaks: Inductive output impedance can resonate with load capacitance, causing frequency response irregularities
• Cable effects: High output impedance makes the system more susceptible to cable capacitance loading

The -3dB frequency is approximately: f-3dB = 1/(2π × Zout × Cload)

3. Can impedance matching improve signal-to-noise ratio?

Yes, proper impedance matching can significantly improve signal-to-noise ratio (SNR) under specific conditions:

• Thermal noise matching: When source resistance equals amplifier noise resistance, noise figure is minimized
• Power matching: In RF systems, impedance matching maximizes signal power transfer while minimizing reflections
• Voltage matching: High impedance inputs reduce current noise contributions

However, the optimal impedance for noise matching may differ from that for power matching. The choice depends on whether the source is voltage-limited or current-limited and the specific noise characteristics of the amplifier.

4. Why do audio systems use different impedance standards than RF systems?

Audio and RF systems use different impedance standards due to their distinct operating requirements:

Audio Systems (typically high impedance):

• Voltage transfer is more important than power transfer
• Long interconnect cables benefit from high impedance to reduce current-induced losses
• Professional audio uses 600Ω balanced lines for noise immunity
• Consumer audio uses 10kΩ+ inputs to minimize loading effects

RF Systems (typically 50Ω or 75Ω):

• Maximum power transfer is critical for efficient transmission
• Characteristic impedance must match transmission lines
• 50Ω provides optimal balance between power handling and loss
• 75Ω is used in video systems for specific cable characteristics and lower loss

5. How do I determine the optimal input impedance for my circuit?

Determining optimal input impedance requires considering multiple factors:

Step 1: Identify the source characteristics

• What is the source's output impedance?
• Is it a voltage source or current source?
• What are the frequency requirements?

Step 2: Define performance priorities

• Maximum voltage transfer: Zin >> Zsource (typically 10:1 ratio)
• Maximum power transfer: Zin = Zsource (conjugate match)
• Minimum noise: Match source resistance to amplifier noise resistance

Step 3: Consider practical constraints

• Component limitations and availability
• Frequency response requirements
• Cost and complexity factors
• Power consumption limitations

Step 4: Simulation and measurement

• Use SPICE simulation to verify performance
• Build prototypes for validation
• Measure actual impedance vs. frequency
• Optimize based on test results

Generally, for most audio and instrumentation applications, an input impedance 10-20 times higher than the source impedance provides good voltage transfer efficiency while maintaining reasonable component values and stability.