Electronics Guide

Frequency Domain Analysis

The frequency domain representation decomposes complex signals into their constituent frequency components. A pure sine wave appears as a single spectral line, while complex waveforms reveal multiple harmonics, sidebands, and potentially unwanted spurious signals. This analysis directly applies Fourier transform principles to real-world signal characterization.

Understanding the relationship between time and frequency domains is crucial. Rapid changes in the time domain correspond to high-frequency components in the spectrum, while slow variations relate to low-frequency content. Spectrum analyzers make these relationships visible and measurable.

Key Performance Parameters

Several critical specifications define spectrum analyzer capabilities:

• Frequency Range: The span of frequencies the instrument can analyze, from kilohertz to hundreds of gigahertz in advanced models
• Resolution Bandwidth (RBW): The narrowest frequency separation the analyzer can distinguish between adjacent signals
• Dynamic Range: The ratio between the largest and smallest signals measurable simultaneously
• Phase Noise: Residual phase modulation of the local oscillator that affects measurement accuracy
• Sweep Time: The duration required to scan across the specified frequency span

Superheterodyne Architecture

The superheterodyne (swept-tuned) spectrum analyzer represents the traditional and still widely used approach. This architecture employs a voltage-controlled oscillator (VCO) that sweeps across the frequency range of interest. Input signals mix with this swept local oscillator to produce an intermediate frequency (IF), which passes through narrow bandwidth filters for resolution.

Key advantages of superheterodyne analyzers include:

• Extremely wide frequency coverage, extending to millimeter-wave frequencies
• Excellent sensitivity due to narrow-band filtering
• High dynamic range from optimized IF filtering
• Superior phase noise performance

The primary limitation involves sweep time—narrow resolution bandwidths require slower sweeps to maintain accuracy, making real-time analysis challenging. However, for most applications requiring high performance across wide frequency ranges, superheterodyne architecture remains the gold standard.

Fast Fourier Transform (FFT) Architecture

FFT-based spectrum analyzers digitize the input signal directly and compute the frequency spectrum mathematically. This approach enables simultaneous analysis of all frequencies within the span, providing true real-time capture capabilities.

FFT analyzer advantages include:

• Real-time analysis of transient and intermittent signals
• Ability to capture brief events that swept analyzers might miss
• Fast measurement speed for narrow spans
• Phase information preservation for vector signal analysis

Modern high-performance spectrum analyzers often combine both architectures, using FFT analysis for real-time capture and superheterodyne architecture for maximum frequency coverage and sensitivity. This hybrid approach provides the best of both technologies.

Resolution Bandwidth (RBW)

Resolution bandwidth determines the analyzer's ability to separate closely spaced frequency components. The RBW filter, typically implemented in the IF stage, defines the minimum frequency separation required to distinguish two signals as separate spectral lines.

Selecting appropriate RBW involves critical tradeoffs:

• Narrow RBW: Provides better frequency resolution and lower noise floor but increases sweep time
• Wide RBW: Enables faster sweeps and capture of wider signals but reduces sensitivity and resolution

For general rule of thumb, set RBW to approximately one-tenth the expected signal bandwidth for accurate amplitude measurements. When measuring narrowband signals near the noise floor, use the narrowest practical RBW to minimize displayed noise and improve sensitivity.

Video Bandwidth (VBW)

Video bandwidth controls post-detection filtering that smooths the displayed trace. While RBW affects the actual measurement, VBW only influences display characteristics by averaging multiple measurements.

Applications for VBW adjustment:

• Noise Reduction: Setting VBW narrower than RBW smooths random noise fluctuations, making signals more visible
• Signal Averaging: Low VBW provides stable displays for noisy signals without affecting actual measurement resolution
• Transient Capture: Wide VBW preserves rapid amplitude variations for pulsed or modulated signals

The VBW-to-RBW ratio typically ranges from 0.1 to 1. A ratio of 0.3 provides good noise smoothing while maintaining reasonable sweep speed for most applications.

Dynamic Range Specifications

Dynamic range defines the spectrum analyzer's ability to measure large and small signals simultaneously. Several dynamic range specifications characterize different aspects of performance:

• Displayed Average Noise Level (DANL): The noise floor establishing the minimum detectable signal
• Third-Order Intercept (TOI): Characterizes intermodulation distortion performance
• Spurious-Free Dynamic Range (SFDR): The ratio between full-scale signal and largest spurious response
• Second Harmonic Distortion: Ratio of fundamental to second harmonic distortion products

Maximum dynamic range occurs when measuring signals well below the analyzer's damage level but well above the noise floor. Input attenuation and preamplifiers optimize dynamic range for specific measurement scenarios.

Sensitivity Optimization

Achieving optimal sensitivity requires careful attention to multiple factors:

• Minimize Input Attenuation: Reduce RF attenuation to lower effective noise floor, but only when input signals won't cause overload
• Use Preamplifiers: External or internal preamps improve sensitivity when measuring very weak signals
• Select Narrow RBW: Noise power is proportional to bandwidth, so narrower RBW lowers displayed noise
• Enable Averaging: Trace averaging or narrow VBW reduces noise fluctuations

For critical low-level measurements, consider electromagnetic interference from the environment. Proper shielding, grounding, and use of high-quality cables significantly impact measurement sensitivity.

Phase Noise Fundamentals

Phase noise appears as a skirt of noise spreading out from both sides of a carrier signal. Measured in dBc/Hz (decibels relative to carrier per hertz of bandwidth), phase noise specifications typically reference specific offset frequencies such as 10 kHz or 100 kHz from the carrier.

Sources of phase noise include:

• Active device noise in oscillators (flicker noise and thermal noise)
• Power supply noise coupling into oscillator circuits
• Mechanical vibrations affecting resonator elements
• Temperature variations modulating oscillator frequency

Measurement Techniques

Accurate phase noise measurement requires consideration of the analyzer's own phase noise. The measured result represents the combined phase noise of the signal under test and the analyzer's local oscillator. For signals with phase noise approaching the analyzer's performance, specialized techniques like phase detector methods become necessary.

Measurement procedure:

1. Set the analyzer to appropriate frequency and span to view the carrier and sidebands
2. Select narrow RBW to resolve close-in phase noise (typically 10 Hz to 1 kHz)
3. Use marker functions to measure noise power at specific offset frequencies
4. Normalize measurements to 1 Hz bandwidth: Phase Noise (dBc/Hz) = Measured Level (dBc) - 10 log(RBW)

Total Harmonic Distortion (THD)

THD expresses the ratio of the sum of harmonic powers to the fundamental power, typically measured in percent or dB. For many applications, the second and third harmonics dominate, but complete characterization may require measurement through the fifth or tenth harmonic.

THD calculation:

THD = sqrt(P₂² + P₃² + P₄² + ... + Pₙ²) / P₁

Where P₁ is fundamental power and P₂ through Pₙ are harmonic powers.

Measurement Considerations

Accurate harmonic measurements require attention to several factors:

• Analyzer Linearity: Ensure input power stays well below compression to avoid measuring analyzer distortion rather than DUT distortion
• Sufficient Dynamic Range: Low distortion devices may produce harmonics 60-80 dB below the fundamental
• Filter Selection: Bandpass filters may be necessary to prevent out-of-band signals from mixing and creating false harmonics
• Frequency Span: Set span wide enough to capture all significant harmonics while maintaining adequate resolution

Third-Order Intermodulation

Third-order intermodulation products are particularly problematic because they appear close to the desired signals. For two input signals at frequencies f₁ and f₂, the critical third-order products appear at:

• 2f₁ - f₂
• 2f₂ - f₁

These products fall near the original signals when f₁ and f₂ are closely spaced, making them difficult to filter and particularly insidious in communication systems.

Two-Tone IMD Testing

The standard two-tone test applies two equal-amplitude signals to the device under test and measures the resulting intermodulation products. The test setup requires:

• Two signal generators with low harmonic distortion
• A combiner to sum the signals
• The spectrum analyzer to measure input and output spectra
• Careful attention to generator and analyzer dynamic range

The third-order intercept point (IP3) extrapolates from measured IMD products to characterize device linearity. Higher IP3 values indicate better linearity and less intermodulation distortion.

Measurement Methodology

Channel power measurement involves:

1. Setting the analyzer span to encompass the channel bandwidth plus guard bands
2. Selecting appropriate RBW (typically 1-3% of channel bandwidth)
3. Enabling channel power marker mode or integration bandwidth
4. Reading integrated power across the defined channel

Modern spectrum analyzers include built-in channel power measurement modes that automate these steps and account for RBW filter shape factors, providing accurate results regardless of modulation type.

Adjacent Channel Power Ratio (ACPR)

ACPR measurements quantify how much power spills into adjacent channels, a critical specification for communication systems. The measurement compares power in the main channel to power in adjacent channels at specified offsets.

High ACPR (low adjacent channel power) indicates good transmitter linearity and filtering. Poor ACPR can cause interference with other users and may violate regulatory requirements. Factors affecting ACPR include amplifier linearity, modulation quality, and filtering effectiveness.

OBW Measurement Procedure

Determining occupied bandwidth requires:

1. Capturing the complete signal spectrum with adequate span
2. Measuring total signal power
3. Finding frequency limits that contain 99% (or specified percentage) of power
4. Calculating the frequency difference between upper and lower limits

The choice of RBW affects measurement accuracy. Too wide, and fine spectral details are lost; too narrow, and measurement time becomes excessive. As a guideline, use RBW approximately 1% of expected occupied bandwidth.

Factors Affecting Occupied Bandwidth

Several design and operational factors influence occupied bandwidth:

• Modulation Type: Different modulation schemes produce different spectral characteristics
• Symbol Rate: Higher data rates generally require wider bandwidth
• Pulse Shaping: Filtering affects spectral roll-off and thus occupied bandwidth
• Amplifier Nonlinearity: Distortion regenerates spectral components that filtering removed
• Phase Noise: Excessive phase noise broadens the spectrum

Real-Time Bandwidth

The real-time bandwidth defines the frequency span over which the analyzer guarantees no signal will be missed. Within this bandwidth, the analyzer continuously digitizes the input, computes FFTs, and analyzes results with zero gaps in time coverage.

Real-time bandwidth is typically much narrower than the analyzer's total frequency range. For example, an analyzer covering DC to 26.5 GHz might offer 160 MHz real-time bandwidth. When analyzing spans wider than real-time bandwidth, the analyzer must sweep, potentially missing brief events.

Applications for Real-Time Analysis

Real-time spectrum analysis excels in several demanding applications:

• Intermittent Interference Detection: Capturing elusive interference that appears sporadically
• Frequency-Hopping Systems: Analyzing signals that rapidly change frequency
• Pulsed RF Characterization: Measuring radar pulses and other transient signals
• Spectrum Monitoring: Recording all activity in a frequency band for regulatory compliance
• EMI Troubleshooting: Identifying intermittent electromagnetic interference sources

Density Display and Spectrograms

Real-time analyzers often include specialized display modes that reveal signal behavior over time. Density displays use color to indicate how frequently signals appear at each frequency, making intermittent signals visible even when rare. Spectrograms show frequency versus time, with color representing amplitude, providing intuitive visualization of signal dynamics.

IQ Data Capture and Analysis

VSA captures in-phase (I) and quadrature (Q) signal components, representing the signal as a vector in the complex plane. This complete representation enables:

• Constellation diagrams showing modulation accuracy
• Error vector magnitude (EVM) measurements quantifying modulation quality
• Symbol timing and carrier frequency error analysis
• Bit error rate (BER) estimation from EVM
• Spectral analysis including phase information

Modulation Analysis

VSA software demodulates signals according to various standards including:

• Cellular standards (5G NR, LTE, WCDMA, GSM)
• Wireless LAN (WiFi 6E, 802.11ax/ac/n)
• Bluetooth and other IoT protocols
• Broadcast standards (DVB, ATSC)
• Custom modulation formats

The analyzer compares received signals against ideal reference signals, identifying impairments such as IQ imbalance, phase noise, amplitude droop, and compression. These insights guide transmitter optimization and troubleshooting.

EMI Standards and Limits

Various regulatory bodies establish EMI limits:

• FCC Part 15: United States regulations for unintentional radiators
• CISPR Standards: International standards for conducted and radiated emissions
• EN Standards: European electromagnetic compatibility requirements
• MIL-STD-461: Military electromagnetic interference requirements

Limits differ for conducted emissions (measured on power and signal cables) versus radiated emissions (measured with antennas), and vary by product class, frequency range, and environment.

EMI Measurement Configuration

EMI precompliance measurements require specific analyzer settings:

• Quasi-Peak Detector: Weighted detection method specified by CISPR standards
• Specified RBW: Standards mandate RBW (typically 9 kHz, 120 kHz, or 1 MHz depending on frequency)
• Appropriate Transducer: Line impedance stabilization networks (LISN) for conducted emissions or calibrated antennas for radiated emissions
• Limit Lines: Display regulatory limits directly on the spectrum for comparison

Modern spectrum analyzers include EMI measurement personalities that automatically configure settings according to selected standards, streamlining precompliance testing.

Transmission Measurements

Connecting the tracking generator output to the device input and the device output to the spectrum analyzer input displays the transmission response (S21). This reveals:

• Filter Characteristics: Passband flatness, insertion loss, and rejection
• Amplifier Gain: Frequency-dependent gain and bandwidth
• Cable Loss: Attenuation versus frequency
• Antenna Response: Return loss and impedance matching

Normalization removes the tracking generator's own frequency response from measurements, displaying only the device's characteristics. This technique involves measuring a thru connection, storing the result, and displaying subsequent measurements relative to this reference.

Reflection Measurements

With an appropriate directional coupler or bridge, the tracking generator setup measures return loss and VSWR. The coupler separates forward and reflected waves, with the reflected signal amplitude indicating impedance matching quality.

Applications include:

• Antenna impedance characterization
• Filter impedance matching verification
• Transmission line integrity testing
• Amplifier input/output match optimization

Gated Spectrum Analysis

The time gate defines a window during which the analyzer captures signal data. Outside this window, signals are ignored. Applications include:

• Pulsed RF Analysis: Measuring only the pulse-on period while excluding pulse-off noise
• TDMA Signal Analysis: Examining individual time slots in time-division systems
• Transient Characterization: Analyzing transmitter turn-on or turn-off behavior
• Interference Isolation: Separating desired signals from time-overlapping interference

Gate Positioning and Width

Proper gate setup requires careful attention to timing. The gate must open after signal stabilization but before turn-off, capturing steady-state behavior. Gate width affects frequency resolution through the time-frequency uncertainty principle—narrower gates provide better time resolution but worse frequency resolution.

Triggering mechanisms synchronize the gate with the signal. External triggers, video triggers, or RF power triggers align gate timing with specific signal events. Trigger delay fine-tunes gate position relative to the trigger event.

Creating Limit Lines

Limit lines consist of amplitude-frequency pairs defining upper and lower boundaries. Modern analyzers support:

• Point-by-point entry for custom shapes
• Standard templates (EMI limits, mask testing)
• Imported data from files or other instruments
• Offset limits derived from measured traces

Multiple limit lines may be active simultaneously, each with independent pass/fail criteria and alarm actions.

Automated Testing and Alarms

When limit testing is enabled, the analyzer continuously compares measured traces against defined limits. Failures trigger programmable actions:

• Visual indicators (screen color changes, failure annotations)
• Audible alarms
• Trace storage for failure documentation
• External control signals for test system integration
• Remote notifications via network interfaces

This automation enables unattended monitoring and high-throughput production testing with immediate failure detection and documentation.

Internal Alignment

Internal alignment (self-calibration) corrects for normal drift in internal references and circuits. This procedure should run:

• After power-on and warm-up (typically 30 minutes)
• When ambient temperature changes significantly
• Periodically during long measurement sessions
• After changing frequency ranges or input configurations

The alignment process disconnects the input, applies internal calibration signals, and measures various parameters to update correction factors. This ensures amplitude accuracy, frequency accuracy, and optimal performance.

Amplitude Calibration

Amplitude accuracy verification uses calibrated signal generators or power sensors. The procedure measures known signal levels and compares results against expected values, generating correction factors or identifying out-of-specification performance.

Key amplitude calibration points include:

• Reference level accuracy across the input range
• Frequency response flatness
• Input attenuation accuracy
• Preamplifier gain accuracy (if applicable)

Frequency Calibration

Frequency accuracy depends on the internal frequency reference, typically a temperature-compensated crystal oscillator (TCXO) or oven-controlled crystal oscillator (OCXO). External reference inputs allow locking to higher-stability references such as GPS-disciplined oscillators or atomic frequency standards.

Frequency calibration verification uses a known frequency source, confirming that displayed frequency matches actual frequency within specified tolerances. For critical applications requiring ppm-level accuracy, external reference locking is essential.

Calibration Intervals and Documentation

Regular calibration maintains measurement integrity. While manufacturers typically recommend annual calibration, actual intervals depend on:

• Measurement criticality and required accuracy
• Operating environment (temperature, vibration, humidity)
• Usage intensity and duty cycle
• Historical drift data from previous calibrations
• Regulatory or quality system requirements

Maintaining calibration records documents measurement traceability to national standards, essential for regulatory compliance and quality certifications. Many organizations maintain calibration databases tracking instrument history, calibration dates, results, and adjustment details.

Optimizing Measurement Speed

Measurement speed becomes critical in production testing and automated systems. Several factors influence sweep time:

• Resolution Bandwidth: Wider RBW enables faster sweeps (sweep time proportional to span squared divided by RBW cubed)
• Frequency Span: Narrower spans reduce sweep time proportionally
• Video Bandwidth: Wider VBW reduces sweep time
• Detector Mode: Peak detection is faster than sample or RMS detection
• Averaging: Reduces or eliminates averaging for faster updates

However, speed optimization must not compromise measurement validity. Always verify that reduced measurement times still provide adequate accuracy for the application.

Noise Floor Reduction

When measuring weak signals, minimize the noise floor through:

• Narrowest practical RBW (noise power proportional to RBW)
• Minimum input attenuation consistent with avoiding overload
• External preamplifiers when signals approach analyzer noise floor
• Averaging or narrow VBW to smooth noise fluctuations
• Shielded test setup minimizing external interference

Avoiding Common Errors

Several measurement errors frequently occur with spectrum analyzers:

• Overload Distortion: Excessive input power creates harmonics and IMD within the analyzer itself. Monitor the input overload indicator and add attenuation when necessary.
• Insufficient Resolution: RBW wider than signal bandwidth produces inaccurate amplitude readings. Use RBW approximately one-tenth signal bandwidth.
• Noise Masking: Weak signals buried in noise floor require sensitivity optimization techniques described above.
• Image Responses: In superheterodyne analyzers, image frequencies can create false signals. Use appropriate input filtering or select different IF configurations.
• Improper Averaging: Averaging intermittent signals makes them appear continuous. Understand signal characteristics before enabling averaging.

Spectrum Analyzer versus Oscilloscope

While oscilloscopes display amplitude versus time and spectrum analyzers display amplitude versus frequency, modern instruments increasingly blur these distinctions. Many oscilloscopes include FFT-based spectrum analysis, and spectrum analyzers may offer time-domain views.

Choose spectrum analyzers when:

• Analyzing high-frequency signals beyond oscilloscope bandwidth
• Measuring small signals requiring excellent sensitivity
• Characterizing harmonic content or spurious signals
• Needing wide dynamic range for simultaneous large and small signals

Oscilloscopes excel at time-domain analysis, capturing transients, and analyzing complex modulation waveforms in the time domain.

Spectrum Analyzer versus Signal Analyzer

Signal analyzers are sophisticated spectrum analyzers with additional demodulation and vector signal analysis capabilities. While basic spectrum analyzers measure amplitude versus frequency, signal analyzers extract modulation parameters, demodulate complex signals, and analyze communication signal quality.

Signal analyzers add:

• Wide-bandwidth IQ data capture
• Standards-based demodulation and analysis
• Advanced triggering on modulation characteristics
• Deep memory for long acquisition records

Software-Defined Spectrum Analysis

Modern spectrum analyzers increasingly rely on software-defined architectures where wide-bandwidth ADCs digitize signals early in the signal path, with subsequent processing performed digitally. This approach enables:

• Feature upgrades through software rather than hardware changes
• Multiple measurement personalities in a single instrument
• Advanced signal processing previously impractical in analog architectures
• Flexibility to adapt to new standards and measurement needs

Millimeter-Wave and Terahertz Analysis

As wireless communications and radar systems push into millimeter-wave frequencies (30-300 GHz) and beyond, spectrum analyzers follow. These ultra-high-frequency analyzers enable:

• 5G millimeter-wave signal analysis
• Automotive radar characterization (77 GHz)
• Satellite communication system testing
• Terahertz imaging and spectroscopy applications

Increased Automation and AI Integration

Artificial intelligence and machine learning enhance spectrum analyzer capabilities:

• Automatic signal classification and identification
• Intelligent measurement setup based on signal characteristics
• Anomaly detection for spectrum monitoring
• Predictive maintenance identifying drift before failures occur