Electronics Guide

Mode-Tuned Operation

In mode-tuned operation, the stirrer is moved to discrete positions and held stationary while measurements are made:

1. Position stirrer at starting angle
2. Allow field to stabilize (several chamber time constants)
3. Perform measurement (power, field strength, or device response)
4. Record data and stirrer position
5. Advance stirrer to next position
6. Repeat until full rotation completed

Mode-tuned operation provides the highest measurement accuracy because each sample is taken at steady-state conditions. It enables correlation between stirrer position and measured values, allowing identification of worst-case positions for equipment under test.

The chamber settles with the time constant τ = Q/(2πf), which for a typical loaded chamber above 1 GHz amounts to a few microseconds. The dwell at each position is therefore set in practice by the response time of the instrumentation and of the equipment under test rather than by the chamber itself, although the chamber term grows at low frequencies where Q is high relative to frequency.

Mode-tuned measurements commonly use on the order of one hundred to four hundred stirrer positions per rotation, which corresponds to angular increments of 3.6 degrees down to 0.9 degree. The number of positions should exceed the number of independent samples the stirrer can actually produce, so that the sequence resolves the correlation structure rather than aliasing it.

Mode-Stirred Operation

In mode-stirred operation, the stirrer rotates continuously while measurements are made:

1. Set stirrer to continuous rotation at specified speed
2. Apply excitation signal
3. Continuously sample measurement data
4. Process samples to extract statistics (mean, maximum, standard deviation)
5. Complete full rotation(s) before stopping

Mode-stirred operation is faster but requires careful attention to measurement bandwidth and sampling rate. The detector bandwidth must be wide enough to follow field variations as the stirrer rotates, and the sampling rate must capture the relevant statistics.

Stirrer speeds of roughly 0.5 to 10 revolutions per minute are common. Faster rotation shortens the test but may drive the field through configurations faster than the detector can follow, which truncates the peaks and biases the maximum low. Slower rotation preserves the statistics at the cost of test duration.

Sample Size Requirements

The number of independent samples determines measurement uncertainty:

• Minimum: IEC 61000-4-21 sets a frequency-dependent minimum number of stirrer positions, a dozen or so at the upper frequencies rising to on the order of fifty in the lowest octaves above the lowest usable frequency (LUF), where mode density is marginal
• Typical: fifty to one hundred independent samples, which leaves a standard uncertainty of roughly 10 to 14 percent, or 0.4 to 0.6 dB, in mean power
• High accuracy: two hundred or more independent samples, bringing that figure below 7 percent, or about 0.3 dB

The number of independent samples is not the number of stirrer positions. It depends on the correlation between adjacent positions, and the shortfall is largest near the LUF, where a stirrer changes the boundary conditions only slightly from one position to the next. A sequence of three hundred sixty positions may yield only a few dozen independent samples at the bottom of the range, while approaching the position count at the top of it. Treating positions as independent samples therefore understates the uncertainty, sometimes by a wide margin.

Combining multiple stirring methods (mechanical, frequency, and source position) can increase the effective number of independent samples without proportionally increasing test time.

Frequency Stepping

When testing across a frequency range, the frequency step size affects both accuracy and efficiency:

• Steps well below the chamber correlation bandwidth, which is of the order of the modal bandwidth f/Q, resolve the chamber response but return little new information per point, since neighboring frequencies remain correlated
• At frequencies well above the LUF, larger steps are acceptable for general characterization
• Logarithmic frequency stepping (constant percentage bandwidth) is common
• Critical frequencies (near device resonances or limit frequencies) may require finer steps

Steps of roughly 0.5 to 2 percent of the center frequency are common in practice. IEC 61000-4-21 prescribes the frequency grid used for chamber validation, with the points spaced most closely in the lowest octaves above the LUF, where chamber behavior changes fastest with frequency.

Measurement Configuration

IEC 61000-4-21 specifies a standard uniformity measurement procedure:

1. Define working volume where equipment under test will be placed
2. Position reference antenna at each of 8 locations (working volume corners)
3. Orient antenna in three orthogonal directions at each location (24 total measurements)
4. At each configuration, record maximum received power over full stirrer rotation
5. Calculate standard deviation of the 24 maximum values

The measurement locations form a rectangular volume with antenna positions at each corner. The working volume should be the maximum region where equipment will be tested. Because the criterion rests on maxima rather than averages, each configuration must be sampled over a full rotation at the number of positions the standard requires for that frequency band.

Uniformity Criteria

IEC 61000-4-21 specifies the maximum standard deviation of the 24 maximum measurements as a function of frequency:

• At and below 100 MHz: Standard deviation not exceeding 4 dB
• 100 to 400 MHz: Tolerance tapers linearly from 4 dB at 100 MHz down to 3 dB at 400 MHz
• Above 400 MHz: Standard deviation not exceeding 3 dB
• Near the LUF: The standard permits the limit to be exceeded at a limited number of frequencies, provided the excess is bounded and documented, recognizing that mode density is marginal near the lowest usable frequency

The wider allowance at the bottom of the range reflects the sparser, less overlapped modes found there. If uniformity does not meet requirements, potential causes include:

• Insufficient mode density (frequency too close to LUF)
• Inadequate stirrer effectiveness
• Direct coupling between transmit and receive antennas
• Loading effects from objects in working volume
• Standing wave patterns from symmetric chamber dimensions

Calibration Frequency

Uniformity validation should be performed:

• Initially after chamber construction or major modification
• Annually as part of routine calibration
• After changes to stirrer, antenna, or chamber configuration
• Whenever measurement validity is questioned

Documentation of uniformity results provides traceability and supports measurement uncertainty analysis.

Chamber Loading Effects on Uniformity

Large equipment under test affects chamber uniformity:

• Increased absorption reduces Q and changes field distribution
• Scattering from equipment may improve or degrade uniformity
• Shadow regions behind large absorbing objects may have reduced fields

When testing large equipment, chamber loss measurements with the equipment in place characterize these effects. Standards require the loading to be measured and bounded so that the reference calibration remains valid, with the bound expressed as a permitted change of a few decibels in chamber insertion loss relative to the empty reference condition. Loading beyond the permitted bound calls for recharacterizing the chamber with the load in place rather than correcting the earlier calibration.

Test Setup

Equipment under test (EUT) setup requires:

1. Position EUT in working volume, away from walls and stirrer
2. Connect EUT cables as in normal operation, routed to penetration panels
3. Establish EUT normal operating condition with monitoring
4. Document EUT configuration including software version and operating mode

EUT orientation is typically not critical due to statistical isotropy, but specific orientations may be required by product standards or customer requirements. Support structures should be non-metallic to minimize field perturbation.

Field Level Establishment

The required field level follows from the chamber calibration factor (CCF), which relates input power to the mean-square electric field:

CCF = mean[|E|²]/P_in

The root-mean-square total field produced by a given input power is therefore:

E_rms = √(CCF P_in)

The calibration factor carries units of V²/m²/W and is determined during chamber validation by measuring the received power at a reference antenna of known efficiency.

Because the field is statistical, several different field quantities can be quoted for the same test, and they differ by several decibels: the rms field averaged over a rotation, the average of the maximum values recorded during validation, and the largest value observed at any single stirrer position. A stated test level is meaningful only when the calibration record says which statistic it refers to, and the same statistic must be used when the drive power is set. Whichever convention applies, excursions above the nominal level occur at individual stirrer positions, and the equipment under test experiences them.

Test Execution

Immunity test procedure:

1. Set frequency to first test point
2. Apply power to achieve required average field level
3. Execute stirring sequence (mode-tuned or mode-stirred)
4. Monitor EUT for performance degradation or malfunction
5. Record any deviations from normal operation
6. Step to next frequency and repeat

Dwell time at each frequency must be sufficient for the EUT to respond to the field and for adequate stirrer sampling. Typical dwell times range from 1 second per stirrer position (mode-tuned) to several full rotations (mode-stirred).

Performance Monitoring

EUT performance monitoring during testing requires:

• Functional parameters relevant to normal operation
• Monitoring circuits isolated from chamber fields (optical links preferred)
• Automatic logging of monitored parameters
• Defined pass/fail criteria before testing begins

Performance criteria typically reference product standards, such as the performance criteria used with IEC 61000-4-3 for general radiated immunity, along with automotive and military requirements, which define acceptable degradation during and after exposure.

Results Interpretation

Interpreting immunity test results requires understanding the statistical nature of the exposure:

• The EUT is exposed to fields from all directions and polarizations during a single stirring sequence
• Worst-case exposure occurs at one or more stirrer positions within the sequence
• Average exposure equals the specified test level when that level is specified as an average
• For exponentially distributed power sampled at one hundred to one thousand independent positions, the expected maximum sits roughly 7 to 9 dB above the mean, and the margin grows only logarithmically with the number of samples

Failure at a specific stirrer position may indicate a directional or polarization sensitivity that can be investigated further with anechoic chamber testing if needed.

Total Radiated Power Measurement

The total radiated power (TRP) is measured using the chamber as an integrating device:

1. Position EUT in working volume with normal operating configuration
2. Operate EUT in mode that produces maximum emissions
3. Measure average received power at reference antenna over stirrer rotation
4. Calculate TRP using chamber calibration factor

The relationship between received power and TRP follows from the aperture relation for an antenna immersed in an isotropic, randomly polarized field, inverted through the same chamber calibration factor used for immunity testing:

TRP = P_rec × (8πη₀/λ²) × (1/η_ant) × (1/CCF)

Here P_rec is the average received power, η_ant is the reference antenna efficiency, and η₀ is the impedance of free space, approximately 377 ohms. The two symbols share a letter but are unrelated quantities. The middle terms undo the reception process: an antenna in a reverberant field presents an angle- and polarization-averaged effective aperture of λ²/(8π), so multiplying the received power by 8πη₀/λ² and dividing by the antenna efficiency recovers the mean-square field in the chamber. Dividing that field by the calibration factor then gives the power the EUT must be radiating to sustain it.

The decomposition depends on which calibration convention the laboratory records. IEC 61000-4-21 chamber validation yields both a field-referenced factor (mean-square field per watt of input power, the form used here) and a dimensionless average received-to-input power ratio. If the chamber is characterized by the power ratio instead, the aperture and antenna-efficiency terms are already embodied in it, and TRP is simply the average received power divided by that ratio. Applying both forms together double-counts the antenna terms and biases the result, so the calibration record must state the convention in use.

Comparison with Limit Specifications

Most EMC emissions limits are specified as field strength at a distance, typically 3 or 10 meters, assuming a reference antenna gain. The equivalent free-space field strength at distance d follows from the total radiated power:

E = √(30 TRP G)/d

Here G is the assumed numeric gain of the equivalent radiator, 1.5 for a short dipole and 1.64 for a half-wave dipole, TRP is in watts, d is in meters, and E is in volts per meter. The constant 30 is the free-space impedance divided by 4π. The conversion presumes that the equipment radiates like that equivalent antenna, which real equipment rarely does, so the result carries an additional uncertainty that no amount of chamber precision removes.

Some standards now include reverberation chamber methods with limits expressed as TRP, avoiding the conversion uncertainty.

Frequency Scanning

Emissions measurements typically scan a frequency range to identify emission peaks:

1. Set measurement receiver to starting frequency
2. Record maximum received power over stirrer rotation
3. Step to next frequency
4. Repeat across entire frequency range
5. Identify frequencies with highest emissions
6. Perform detailed measurements at peak frequencies

Initial scans may use wider frequency steps for efficiency, with finer steps near peaks for accurate level determination.

Advantages and Considerations

Reverberation chamber emissions testing offers:

• Speed: No need to rotate EUT or scan antenna position
• Total power: Captures all radiated energy regardless of direction
• Repeatability: Less sensitive to EUT positioning

However, limitations include:

• No directional information about emissions
• Results not directly comparable to anechoic measurements
• May not be accepted for all compliance purposes
• LUF limits low-frequency coverage

Enclosure Shielding Measurement

For enclosure shielding effectiveness (SE):

1. Place receive antenna inside enclosure under test
2. Position enclosure in chamber working volume
3. Measure average received power with the enclosure closed, P_shielded
4. Remove enclosure, measure average received power at same location, P_unshielded
5. Calculate the shielding effectiveness in decibels

The shielding effectiveness is the ratio of the two averaged powers:

SE = 10 log₁₀(P_unshielded/P_shielded)

Multiple stirrer rotations and frequency points characterize SE across the test range. Both power values are averages over the stirring sequence, and the shielded measurement often approaches the noise floor of the receiver, so the dynamic range of the instrumentation sets the largest shielding effectiveness the method can resolve. Results represent the average SE over all angles of incidence and polarizations.

Nested Reverberation Chamber Method

For larger enclosures that operate as reverberation chambers themselves, the nested chamber method applies:

1. Place enclosure (inner chamber) inside main reverberation chamber (outer chamber)
2. Excite outer chamber with transmit antenna
3. Measure field inside inner chamber with receive antenna
4. Stir both outer and inner chambers (if inner has stirrer)
5. Compare to reference measurement without inner enclosure

This method accounts for the mode structure of the inner enclosure and provides results applicable to real-world shielded room performance.

Cable and Connector Shielding

Shielded cable effectiveness is characterized by transfer impedance, measurable in a reverberation chamber:

1. Install cable sample through chamber wall with proper shield terminations
2. Illuminate cable shield with chamber field
3. Measure voltage coupled to inner conductor
4. Calculate transfer impedance from field strength and coupled voltage

This method tests the cable under realistic multi-path illumination conditions that may reveal weaknesses not apparent in traditional single-direction testing.

Material Shielding Effectiveness

Shielding effectiveness of materials can be measured using aperture methods:

1. Create a reference aperture in a shielded enclosure
2. Measure power transmitted through open aperture, P_open
3. Cover aperture with material under test
4. Measure power transmitted through covered aperture, P_material
5. Calculate the shielding effectiveness in decibels

The result takes the same form as the enclosure measurement:

SE = 10 log₁₀(P_open/P_material)

Results include contributions from both material properties and aperture diffraction effects. The method is most appropriate for materials used to cover openings in shielded enclosures.

Data Recording

Measurements should record:

• Received power (or field strength) at each stirrer position
• Stirrer position angle or index
• Frequency for each measurement set
• Forward and reflected power at transmit antenna
• Environmental conditions (temperature, humidity)
• EUT status and monitored parameters (for immunity)

Raw data should be preserved for subsequent analysis, even when only summary statistics are needed for reports.

Statistical Quantities

Take N power samples P_i recorded over one stirring sequence. Four quantities summarize them. The mean power is the arithmetic average:

P_mean = (1/N)∑_i=1^NP_i

The maximum power is the largest sample in the sequence:

P_max = max(P₁, P₂, …, P_N)

The sample standard deviation measures the spread about the mean:

σ = √((1/(N − 1))∑_i=1^N(P_i − P_mean)²)

The coefficient of variation expresses that spread relative to the mean:

CV = σ/P_mean

For an ideal chamber with exponentially distributed power samples, CV approaches 1, because the standard deviation of an exponential distribution equals its mean. A value well below 1 points to a deterministic component such as direct coupling between the antennas. A value well above 1 usually means the samples are too few or too strongly correlated for the spread to be estimated reliably. These statistics must be computed on linear power values rather than on decibels, since averaging decibel values biases the mean low.

Distribution Verification

Verifying that measured data follows expected distributions validates chamber operation:

• Chi-squared test: compares the binned measured distribution against the theoretical exponential distribution
• Kolmogorov-Smirnov test: compares the empirical cumulative distribution function against the theoretical one and needs no binning
• Probability plots: show graphically where the data departs from the theoretical distribution, usually in the tail that matters most for maximum values

Departures from expected distributions may indicate insufficient mode density, inadequate stirring, direct coupling, or excessive loading. Goodness-of-fit tests assume independent samples, so they must be applied to a decorrelated subset of the recorded positions rather than to every position sampled.

Outlier Detection

Statistical outliers can affect results and should be investigated:

• A Gaussian rule of thumb misleads here. For exponentially distributed power, a sample three standard deviations above the mean is simply a sample four times the mean, which occurs with probability e⁻⁴, about 2 percent, so a handful in a hundred samples is expected rather than suspicious
• Consistent outliers at specific stirrer positions suggest direct coupling
• Outliers at specific frequencies may indicate chamber resonances

Outliers should not be automatically removed; they may represent valid worst-case conditions relevant to the test objective.

Uncertainty Sources

Major uncertainty contributors include:

• Statistical sampling: Finite number of independent samples creates uncertainty in estimated mean and maximum values
• Field uniformity: Spatial variation within working volume
• Antenna calibration: Uncertainty in reference antenna factors
• Instrumentation: Power meter, network analyzer, and receiver uncertainties
• Mismatch: Reflections between components
• Loading effects: EUT loading changes from calibration conditions
• Chamber calibration: Uncertainty in CCF determination

Statistical Uncertainty

The statistical uncertainty in the estimated mean power depends on the number of independent samples N_ind, not on the number of stirrer positions recorded:

u(P_mean)/P_mean = 1/√N_ind

One hundred independent samples therefore leave a relative standard uncertainty of 10 percent, or 0.4 dB, and four hundred leave 5 percent, or 0.2 dB. Because power is proportional to the square of field amplitude, the corresponding relative uncertainty in amplitude is half as large:

u(E)/E ≈ 1/(2√N_ind)

Maximum values behave differently. The largest of N_ind independent, exponentially distributed samples follows an extreme value (Gumbel) distribution, whose expected value exceeds the mean power by a factor close to ln(N_ind) + 0.577 and whose standard deviation stays near 1.28 times the mean power however many samples are taken. The relative uncertainty in an observed maximum therefore improves only logarithmically:

u(P_max)/P_max ≈ 1.28/(ln(N_ind) + 0.577)

For one hundred independent samples that is about 25 percent, close to 1 dB, and quadrupling the sample count to four hundred reduces it only to about 20 percent. Sampling harder does not fix a maximum-based measurement. The practical remedy is to average the maxima from several independent rotations, since the mean of M such maxima has a standard error smaller by a factor of √M. That averaging is precisely what the field uniformity procedure performs when it works from the maxima recorded at twenty-four antenna configurations.

Combined Uncertainty

Individual uncertainty components combine as a root sum of squares, provided they are independent of one another:

u_c = √(u₁² + u₂² + u₃² + …)

The independence condition is not a formality. Contributions that share a common cause are correlated, and quadrature summation then understates the result. Two field measurements traceable to the same antenna calibration are one example, and mismatch terms that involve the same connector pair are another. A correlated pair requires an explicit covariance term, or, as a conservative bound, the two contributions may be added linearly instead.

The expanded uncertainty for a 95 percent level of confidence uses the coverage factor k = 2:

U = 2u_c

Published laboratory budgets for reverberation chamber work commonly report expanded uncertainties of roughly 3 to 4 dB for immunity test levels, 4 to 6 dB for total radiated power, and 2 to 4 dB for shielding effectiveness. These figures vary with facility, frequency, and the number of independent samples, so each laboratory must build its own budget rather than adopt published values.

Uncertainty Budget Documentation

A complete uncertainty budget should document:

• All identified uncertainty sources
• Estimated magnitude of each source
• Type (A or B) classification
• Probability distribution assumed
• Sensitivity coefficients if applicable
• Correlations between contributions, where any exist
• Combined and expanded uncertainty

Uncertainty analysis per GUM (Guide to the Expression of Uncertainty in Measurement) principles provides traceable, defensible uncertainty estimates.

Measurement Procedure

The standard approach derives absorption cross-section from the change in the chamber time constant when the object is introduced. The chamber time constant is obtained either from the chamber quality factor (Q) measured in the frequency domain or, more directly, from the exponential decay of the power-delay profile measured in the time domain.

1. Measure the chamber time constant with the chamber empty, τ_empty
2. Place the object under test in the working volume
3. Measure the chamber time constant with the object present, τ_loaded
4. Calculate absorption cross-section from the difference in inverse time constants

The average absorption cross-section of the object is then:

σ_a = (V/c₀)(1/τ_loaded − 1/τ_empty)

Here V is the chamber volume and c₀ is the speed of light, giving a cross-section in square meters. Each inverse time constant equals the total power loss rate of the chamber, so their difference isolates the loss added by the object. Because absorption shortens the time constant, τ_loaded is smaller than τ_empty and the result is positive.

Since the time constant and the quality factor are related by τ = Q/(2πf), the same quantity may be written in terms of the measured quality factors:

σ_a = (2πV/λ)(1/Q_loaded − 1/Q_empty)

Average received-power measurements yield the same result, because the steady-state received power is proportional to the time constant. The time-constant form is preferred because it avoids the need for an absolute power calibration; only the shape of the decay matters, not its amplitude.

Applications

Absorption cross-section measurements are used for:

• Characterizing loading for chamber calibration correction
• Dosimetry for biological exposure studies
• Material absorber characterization
• Antenna efficiency measurement

The technique provides absorption data averaged over all angles and polarizations, complementing single-angle measurements in anechoic chambers.