14.1 Spectrum Analyser Architecture, Operation, and Spectral Purity

14.1 Spectrum Analyser Architecture, Operation, and Spectral Purity

Radio frequency (RF) engineering requires evaluating signals across two complementary perspectives: the time domain and the frequency domain. While an oscilloscope graphs instantaneous voltage as a function of time, complex multi-frequency RF phenomena—such as harmonic emissions, intermodulation distortion (IMD), sideband splatter, and phase noise skirts—are exceedingly difficult or impossible to quantify from an oscilloscope trace. The spectrum analyser is the preeminent laboratory instrument for frequency-domain characterisation, decomposing an incoming waveform into its individual spectral constituents and graphing signal power against frequency.

   Time Domain (Oscilloscope)                 Frequency Domain (Spectrum Analyser)
   Voltage vs. Time                           Power (dBm) vs. Frequency (Hz)

     V ^        /\          /\                  P ^  Fundamental
       |       /  \        /  \                   |     | 
       |  /\  /    \  /\  /    \                  |     |       2nd Harm   3rd Harm
       +--/-\-/------\/--/-\------>               |     |          |          |
      0| /   V        \ /   V       Time          |    |||        |||        |||
       v               v                          +----|||--------|||--------|||----->
                                                 Ref  f_0        2f_0       3f_0   Freq

The mathematical bridge connecting these two domains is the Fourier Transform. Fourier analysis represents a periodic waveform by its mean (DC component) plus harmonically related sinusoidal components with their respective amplitudes and phases. A pure sine wave in the time domain yields a solitary discrete spectral line (a Dirac delta function) in the frequency domain. Conversely, non-sinusoidal waveforms—such as square waves, pulses, or overdriven amplifier outputs—contain rich arrays of harmonics extending far into the electromagnetic spectrum.

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Swept-Tuned Superheterodyne Spectrum Analyser Architecture

Although modern real-time and Fast Fourier Transform (FFT) spectrum analysers exist, the fundamental architecture underlying high-performance RF spectrum analysers is the swept-tuned superheterodyne receiver. This topology converts a wide swath of input radio frequencies into a fixed intermediate frequency (IF) where precision narrow-band filtering, amplification, and detection take place.

                  Conventional Swept-Tuned Analyser: Signal Path

 RF --> [Input attenuator] --> [LPF/preselector] --> [1st mixer]
                                                        ^    |
                                                  Swept LO   v
                                                        [1st IF filter]
                                                             |
                                                  [Further conversion]
                                                             |
                                                [Final IF / RBW filter]
                                                             |
                                              [Log amp / envelope detector]
                                                             |
                                               [VBW filter / ADC] --> Display

 Sweep control --> Swept LO; the same sweep supplies the frequency axis.

Detailed Analysis of Internal Functional Blocks

1. Input Step Attenuator ($0\text{ to }50-70\text{ dB}$): The input attenuator reduces the level reaching the mixer to control overload, compression and internally generated distortion. The appropriate mixer level depends on the analyser and the required distortion measurement; it is not a universal threshold. Input attenuation and IF gain are normally coupled to the reference-level setting so that displayed amplitudes remain calibrated. Too much attenuation raises the input-referred noise floor.

2. Input Low-Pass Filter / Preselector: To prevent image responses and spurious harmonic mixing from reaching the first IF, input signals pass through a low-pass or tunable tracking bandpass filter (preselector). In modern microwave analysers, this filter prevents signals above the analyser's first conversion band from entering the mixer.

3. First Mixer and Swept Local Oscillator (LO): The mixer combines the input RF signal ($f_{\text{RF}}$) with the output of a swept Voltage-Controlled Oscillator (VCO), typically a Yttrium Iron Garnet (YIG) tuned oscillator or a fractional-N PLL synthesiser. A sawtooth ramp generator sweeps the LO frequency linearly across a designated range. High-performance analysers employ an up-converting architecture, setting the first intermediate frequency ($f_{\text{IF}}$) higher than the highest input tuning frequency (e.g., an IF of $3.1\text{ GHz}$ for an analyser covering $0\text{ to }3.0\text{ GHz}$). Placing the IF above the input band pushes the image frequency ($f_{\text{image}} = f_{\text{LO}} + f_{\text{IF}}$) up into microwave territory ($> 6.2\text{ GHz}$), where it can be eliminated with a simple fixed low-pass input filter.

4. Intermediate Frequency (IF) Filter — Resolution Bandwidth (RBW): The mixed signal is directed through a chain of bandpass filters. The narrowest filter in the chain defines the Resolution Bandwidth (RBW). The RBW filter is typically implemented with a Gaussian response shape to prevent ringing and overshoot during continuous sweeping. The bandwidth of this filter dictates the analyser's ability to separate closely spaced frequency components.

5. Logarithmic Amplifier: Because RF signal powers span orders of magnitude—from microwatts to hundreds of watts, or nanowatts in receiver testing—a linear voltage display would compress weak signals into the baseline noise. The logarithmic amplifier applies a non-linear transfer function ($V_{\text{out}} \propto \log_{10}(V_{\text{in}})$), compressing a $100\text{ dB}$ power dynamic range into a standard display grid calibrated in decibels relative to one milliwatt ($\text{dBm}$) at $10\text{ dB}$ per vertical division.

6. Envelope Detector: An envelope detector removes the IF carrier and produces a voltage following its amplitude envelope. The selected detector and subsequent averaging/processing determine the displayed signal level; envelope voltage is not itself a direct average-power measurement.

7. Video Filter — Video Bandwidth (VBW): Following envelope detection, the signal is a baseband direct-current voltage fluctuating with modulation or noise. It passes through a variable low-pass filter designated the Video Filter, whose cut-off frequency is the Video Bandwidth (VBW). The video filter smooths rapid, high-frequency noise spikes, acting as a signal averager to clarify low-level signals obscured near the noise floor.

8. Display Generator / ADC: An Analog-to-Digital Converter (ADC) samples the detected video voltage. In synchronism with the horizontal sweep ramp, the display plots signal amplitude on the vertical Y-axis (in $\text{dBm}$ or $\text{dB}\mu\text{V}$) against frequency on the horizontal X-axis (in $\text{kHz}$, $\text{MHz}$, or $\text{GHz}$).

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Operating Controls and Measurement Constraints

Operating a spectrum analyser requires balancing three interconnected parameters: Span, Resolution Bandwidth (RBW), and Sweep Time ($T_{\text{sweep}}$). Adjusting any one parameter directly affects the physical validity of the measurement.

                               The RBW Filtering Effect

     Wide RBW (e.g., 10 kHz)                      Narrow RBW (e.g., 300 Hz)
     Cannot resolve 1 kHz tones                   Resolves both tones + IMD products

     Power ^                                      Power ^
           |       ____                                 |       /\      /\
           |      /    \  <-- Merged peak               |      /  \    /  \   <-- Deep valley
           |     /      \                               |     /    \  /    \      revealed
           |    /        \                              |    /      \/      \
           +---/----------\---------->                  +---/----------------\----->
              f_1        f_2    Freq                       f_1              f_2   Freq

1. Resolution Bandwidth (RBW) and Frequency Resolution

The RBW setting defines the frequency resolution of the analyser. When two equal-amplitude sinusoidal signals spaced by $\Delta f$ enter the analyser, their individual responses merge into a single broad peak unless the RBW is narrower than their separation:

$\text{RBW} \le \Delta f$

In practical amateur transmitter testing—such as an audio two-tone intermodulation test where two tones are separated by $1.0\text{ kHz}$—an RBW of $3\text{ kHz}$ or $10\text{ kHz}$ completely obscures the individual tones, showing only an aggregated hump. To display a deep valley (at least $10\text{ to }20\text{ dB}$ drop) between the $1\text{ kHz}$ tones and expose the adjacent 3rd-order IMD sidebands, the operator must select an $\text{RBW} \le 300\text{ Hz}$ (or $100\text{ Hz}$).

2. The Sweep Time Constraint and Filter Ringing

An IF bandpass filter is a physical tuned resonator possessing stored energy and a finite rise/settling time. The time required for the Gaussian IF filter to charge up to full amplitude when an RF signal sweeps across its passband is inversely proportional to the filter's bandwidth:

$t_{\text{settle}} \approx \frac{1}{\text{RBW}}$

If the local oscillator sweeps across the filter's passband faster than the filter can respond, energy cannot build up to its true steady-state level. The sweep velocity is defined as the frequency span divided by the sweep time ($\text{Span} / T_{\text{sweep}}$ in $\text{Hz/s}$). To avoid distortion, the sweep velocity must not exceed a fraction of the filter bandwidth squared:

$\frac{\text{Span}}{T_{\text{sweep}}} \le \frac{\text{RBW}^2}{k}$

Rearranging yields the fundamental Minimum Sweep Time Formula:

$T_{\text{sweep}} \ge k \cdot \frac{\text{Span}}{\text{RBW}^2}$

where $k$ is a filter-response constant, typically $2.0$ to $3.0$ for conventional near-Gaussian analog resolution filters. FFT analysis processes frequency blocks and can be much faster; its acquisition time is not obtained merely by substituting a smaller fixed $k$ into this swept-filter equation.

3. Displayed Average Noise Floor (DANL)

The Displayed Average Noise Floor (DANL) represents the internal thermal noise floor of the spectrum analyser, setting the absolute limit on the weakest signals the instrument can detect. Thermal noise power is governed by Johnson-Nyquist physics:

$P_n = k \cdot T \cdot B$

where $k$ is Boltzmann's constant ($1.38 \times 10^{-23}\text{ J/K}$), $T$ is temperature in Kelvin, and $B$ is the measurement bandwidth, which is determined directly by the RBW.

Expressed in decibels relative to one milliwatt:

$\text{DANL} \propto 10 \log_{10}(\text{RBW})$

Furthermore, the input step attenuator directly degrades DANL. Inserting $20\text{ dB}$ of input attenuation attenuates external noise and signals equally while internal mixer noise remains constant, raising the effective noise floor on the screen by $20\text{ dB}$. Therefore, to detect microvolt-level signals, set input attenuation to $0\text{ dB}$ (or use an internal preamplifier) and select the narrowest practical RBW.

4. Video Bandwidth (VBW) vs. Resolution Bandwidth (RBW)

A common misconception is confusing RBW with Video Bandwidth (VBW):

Selecting a VBW significantly smaller than RBW (e.g., $\text{VBW} = 0.1 \times \text{RBW}$) replaces a noisy, jagged noise band ($5-8\text{ dB}$ peak-to-peak variation) with a clean, razor-thin line representing the true mathematical mean noise level.

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Practical Amateur Radio Spectral Measurements

Harmonic measurement
Power ^
    |           |
    |           |
    |           |             |             |
    +-----------+-------------+-------------+----------------> Frequency
               f0            2f0           3f0

Compare each harmonic with the wanted signal using the applicable
section15 frequency/power-dependent requirement.

Equal-tone IMD spectrum
PEP reference: 6.02 dB above either equal wanted tone
    | - - - - - - - - - - - - - - - - - - - - - - -
    |                   |             |
    |                   |             |
    |     |             |             |             |
    +-----+-------------+-------------+-------------+--------> Frequency
       2f1-f2          f1            f2          2f2-f1

Each outer third-order product is one tone-spacing beyond the wanted pair.

1. Harmonic Attenuation and ACMA Compliance

Non-linear transmitter stages generate harmonics at integer multiples of the wanted frequency. For operation under the Radiocommunications (Amateur Stations) Class Licence 2023, section 15 requires spurious emissions to be attenuated below the power within the emission's necessary bandwidth, supplied to the antenna transmission line, by:

• Below $30\text{ MHz}$: the lesser of $43 + 10\log_{10}(pX)$ dB and $50\text{ dB}$, where $pX$ is PEP in watts.
• At or above $30\text{ MHz}$: the lesser of $43 + 10\log_{10}(P)$ dB and $70\text{ dB}$, where $P$ is the power in watts supplied to the antenna transmission line. There is no $25\text{ W}$ breakpoint in this rule.

Measurement Procedure:

1. Rated Attenuation: Never connect a power transmitter directly to the analyser. Use a suitably rated $50\ \Omega$ power attenuator, or a calibrated coupler with the main line terminated in a rated load. For example, $100\text{ W}$ ($+50\text{ dBm}$) through $40\text{ dB}$ attenuation gives $+10\text{ dBm}$ at the analyser connector. Check its actual input/DC limits and select sufficient internal attenuation for a linear mixer-level measurement.
2. Reference and Frequency Response: Measure a steady carrier into the load. Set the reference level and span to display the fundamental and required harmonics, with suitable RBW and automatic sweep time. Account for the attenuator/coupler and cable response at each frequency; equal nominal attenuation does not establish equal calibrated response.
3. Delta Markers and Distortion Check: Compare each harmonic with the fundamental using delta markers and the path corrections. Repeat with more analyser input attenuation: an external component retains its corrected input level, whereas an internally generated distortion product changes. Ensure the harmonic remains above the noise before accepting the result.

2. Measuring Intermodulation Distortion (IMD) in SSB Transmitters

Single Sideband (SSB) requires linear amplification. Non-linearities in RF power transistors generate mixing between spectral components. In standard two-tone testing, two non-harmonically related audio tones (such as $700\text{ Hz}$ and $1900\text{ Hz}$, separated by $1200\text{ Hz}$) are injected into the transmitter microphone input, producing two RF carrier tones at $f_1$ and $f_2$.

Non-linear power amplifier transfer curves generate odd-order mixing products that fall directly within or immediately adjacent to the transmitter passband:

• Third-Order Products ($2f_1 - f_2$ and $2f_2 - f_1$): Located on either side of the two tones, spaced by exactly $1.2\text{ kHz}$.
• Fifth-Order Products ($3f_1 - 2f_2$ and $3f_2 - 2f_1$): Spaced by $2.4\text{ kHz}$.

The Crucial PEP Reference Distinction:

When quantifying IMD, two reference conventions exist in engineering:

1. Referenced to One of the Two Equal Tones (dBc): This is read directly off the spectrum analyser screen as the height difference between the peak of tone $f_1$ and the peak of the 3rd-order product ($2f_1 - f_2$). In high-grade amateur equipment, this ratio is typically $-30\text{ dBc}$ to $-36\text{ dBc}$.
2. Referenced to Peak Envelope Power (PEP): Because two equal tones combining in phase double the peak voltage ($V_{\text{PEP}} = 2 V_{\text{single}}$), the peak envelope power is four times the single-tone average power ($+6\text{ dB}$ higher):

$P_{\text{PEP}} = 4P_{\text{single}}, \qquad P_{\text{PEP}}\text{ (dBm)} = P_{\text{single}}\text{ (dBm)} + 6.02\text{ dB}$

3. Local Oscillator Phase Noise Skirts

No real-world oscillator generates an infinitely thin spectral line. Phase fluctuations and thermal noise modulate the oscillator, creating symmetrical noise "skirts" spreading out on either side of the carrier. This is phase noise, quantified in decibels relative to the carrier per unit bandwidth:

$\mathcal{L}(\Delta f) \quad \text{in } \text{dBc/Hz}$

at a specified frequency offset $\Delta f$ (such as $10\text{ kHz}$ or $100\text{ kHz}$).

In amateur radio receivers, excessive local oscillator phase noise causes reciprocal mixing: when a strong adjacent-channel signal (e.g., $20\text{ kHz}$ away in a contest) enters the mixer, the LO phase noise skirts mix with the strong signal, transferring noise directly into the receiver's IF passband and completely masking weak desired signals.

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Step-by-Step Worked Measurement Calculations

Worked Example 1: Minimum Sweep Time Calculation

An operator is conducting an in-depth spectral analysis of an HF transmitter over a span of $\text{Span} = 500\text{ kHz}$ to inspect sideband splatter. To clearly resolve $1\text{ kHz}$ modulation products, the Resolution Bandwidth is set to $\text{RBW} = 300\text{ Hz}$. The analyser uses an analog Gaussian filter with shape constant $k = 2.5$. Calculate the minimum sweep time required to prevent uncalibrated filter ringing and amplitude compression.

Calculation:

$T_{\text{sweep}} \ge k \cdot \frac{\text{Span}}{\text{RBW}^2}$

Substitute the known values:

$T_{\text{sweep}} \ge 2.5 \cdot \frac{500 \times 10^3\text{ Hz}}{(300\text{ Hz})^2}$

$(300)^2 = 90{,}000\text{ Hz}^2$

$T_{\text{sweep}} \ge 2.5 \cdot \frac{500{,}000}{90{,}000} = 2.5 \cdot 5.5556 \approx 13.89\text{ seconds}$

Result: The sweep time must be set to at least $14\text{ seconds}$. Forcing a $1$-second or $500\text{ ms}$ sweep would result in severe amplitude errors and illuminate the "UNCAL" indicator.

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Worked Example 2: DANL Noise Floor Reduction

A spectrum analyser is configured with $\text{RBW} = 100\text{ kHz}$, displaying an average noise floor of $-95\text{ dBm}$. To detect a weak spurious emission at $-120\text{ dBm}$, the operator reduces the RBW to $100\text{ Hz}$. What is the new Displayed Average Noise Floor, and will the spurious signal be visible?

Calculation:

1. Determine the ratio of bandwidth reduction:

$\text{Ratio} = \frac{\text{RBW}_{\text{new}}}{\text{RBW}_{\text{initial}}} = \frac{100\text{ Hz}}{100{,}000\text{ Hz}} = 10^{-3}$

1. Compute the noise floor change in decibels:

$\Delta P_{\text{noise}} = 10 \log_{10}(10^{-3}) = -30\text{ dB}$

1. Calculate the new DANL:

$\text{DANL}_{\text{new}} = -95\text{ dBm} + (-30\text{ dB}) = -125\text{ dBm}$

Result: The noise floor drops by $30\text{ dB}$ to $-125\text{ dBm}$. The $-120\text{ dBm}$ spurious emission will be clearly visible, standing $5\text{ dB}$ above the noise floor.

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Worked Example 3: Harmonic Compliance Calculation

An amateur linear amplifier delivers $100\text{ W}$ ($+50\text{ dBm}$) of RF power at $7.10\text{ MHz}$ into a $40\text{ dB}$ power attenuator feeding a spectrum analyser. The fundamental signal registers at $+10\text{ dBm}$ on the screen. The second harmonic at $14.20\text{ MHz}$ registers at $-53\text{ dBm}$ on the screen. Determine:

1. The attenuation of the second harmonic relative to the carrier ($\text{dBc}$).
2. Whether this second harmonic meets the applicable below-30-MHz class-licence attenuation requirement, assuming the measurement path is calibrated at both frequencies.

Calculation:

1. Compute the relative harmonic attenuation:

$\text{Suppression (dBc)} = P_{\text{harmonic}} - P_{\text{fundamental}} = -53\text{ dBm} - (+10\text{ dBm}) = -63\text{ dBc}$

1. Evaluate regulatory compliance: For $100\text{ W}$ PEP below $30\text{ MHz}$, section 15 requires the lesser of $43 + 10\log_{10}(100) = 63\text{ dB}$ and $50\text{ dB}$: therefore $50\text{ dB}$.

Result: This second harmonic is $63\text{ dB}$ below the wanted signal, a $13\text{ dB}$ margin over that requirement. This checks the measured harmonic under the stated calibration assumptions; other spurious emissions and licence conditions must be checked separately.

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Comparison Table: Spectrum Analyser Front-Panel Controls