The amplitude-frequency characteristic experiment measures how a system's output amplitude responds to input signals across a defined frequency range, producing the frequency response curve that is essential for evaluating amplifiers, filters, sensors, and mechanical structures. This guide walks through the complete experimental procedure step by step, covering instrumentation requirements, measurement methods, applicable international standards, and practical techniques for achieving accurate and repeatable results in both laboratory and accredited third-party laboratory environments.
Technical Overview
The amplitude-frequency characteristic describes the ratio of a system's steady-state output amplitude to its input amplitude as a function of excitation frequency. Mathematically, it is the magnitude of the frequency response function |H(jω)|, typically expressed in decibels and plotted against a logarithmic frequency axis to form the magnitude portion of a Bode diagram. The resulting curve reveals how a device or structure transmits, attenuates, or amplifies signals at different frequencies.
The experiment is governed by several international and national standards, including the ISO 16063 series for vibration transducer calibration, ISO 7626 for mechanical mobility measurements, IEC 61672 and IEC 60268 for electroacoustic equipment, GB/T 13823 for vibration and shock sensor calibration methods, and GB/T 2423.10 for sinusoidal vibration testing. Electrical safety of the measurement setup should conform to IEC 61010-1.
Key quantities extracted from the amplitude-frequency curve include:
- Passband gain and passband flatness (ripple)
- Lower and upper cutoff frequencies at the -3 dB points
- Bandwidth between cutoff frequencies
- Resonant frequency, peak gain, and quality factor (Q)
- Stopband attenuation and roll-off slope
- Sensitivity deviation over the operating frequency range
Testing Samples
Electronic Circuits and Modules
RC, RL, and RLC filter networks, operational amplifier stages, audio power amplifiers, equalizers, anti-aliasing filters, and communication front-end modules are the most common specimens. These samples are evaluated to verify that gain flatness, cutoff frequencies, and attenuation slopes match the design targets.
Sensors and Transducers
Piezoelectric accelerometers, condenser and MEMS microphones, pressure sensors, and proximity probes are tested to characterize their sensitivity versus frequency, including usable bandwidth and resonance locations. Calibration-oriented testing follows the ISO 16063 series and GB/T 13823.
Electroacoustic Devices
Loudspeakers, headphones, microphones, and sound level meters are measured in accordance with the IEC 60268 series and IEC 61672 to determine their frequency response over the audible range, typically 20 Hz to 20 kHz.
Mechanical Structures and Assemblies
Beams, brackets, printed circuit board assemblies, housings, and mounted components are subjected to swept-sine excitation on electrodynamic shakers to identify structural resonances and transmissibility, following GB/T 2423.10 and ISO 7626. This helps engineers avoid resonance-induced fatigue and malfunction.
Testing Items
Depending on the specimen type, the amplitude-frequency characteristic experiment quantifies the following items:
- Mid-band or reference-frequency gain, and gain flatness across the passband
- Upper and lower cutoff frequencies defined at the -3 dB attenuation points
- -3 dB bandwidth and, for band-pass responses, center frequency
- Resonant frequencies and peak magnification factors for structures and sensors
- Stopband insertion loss and attenuation slope in dB per decade or dB per octave
- Transmissibility and amplification regions for vibration-isolated assemblies
- Amplitude linearity checks at spot frequencies to confirm operation in the linear range
Testing Methods
Step 1: Preparation and Experimental Setup
- Verify that all instruments — signal generator, oscilloscope or AC voltmeter, dynamic signal analyzer, shaker controller, and conditioning amplifiers — hold valid calibration traceable to national metrology institutes.
- Warm up electronic instruments for the manufacturer-specified stabilization time to eliminate thermal drift.
- Define the frequency span of interest (for example, 10 Hz to 100 kHz for circuits, or 5 Hz to 2 kHz for vibration tests) and select logarithmically spaced measurement points, typically 3 to 10 points per decade with denser spacing near expected cutoff or resonance.
- Set the excitation amplitude low enough to keep the specimen in its linear operating region, yet high enough to maintain adequate signal-to-noise ratio.
- Confirm proper impedance matching, grounding, and shielding to suppress hum and electromagnetic interference, and observe electrical safety practices per IEC 61010-1.
- Record ambient conditions (temperature and humidity), instrument model numbers, and cable configurations for the test report.
Step 2: Point-by-Point Sine Excitation Method
- Connect the function generator to the specimen input and the measurement instrument to the specimen output, keeping lead lengths short to minimize parasitic effects.
- Set the generator to the lowest frequency in the plan and adjust the input to the chosen reference amplitude (for example, 1 Vrms), monitoring it continuously with a second channel or voltmeter.
- Allow the output to reach steady state, then record the output amplitude and compute the gain as Vout/Vin; convert to decibels using 20 × log10(Vout/Vin).
- Step to the next frequency point, restore the input amplitude if it has drifted, and repeat the measurement.
- Add intermediate points wherever the curve changes rapidly, such as around cutoff frequencies or resonance peaks, to capture the true shape.
- Tabulate frequency, input amplitude, output amplitude, and computed gain, then plot gain in dB versus frequency on semilogarithmic axes.
- Determine the -3 dB cutoff points, bandwidth, resonant frequency, and peak gain from the curve or the tabulated data.
Step 3: Swept-Sine Measurement Using a Frequency Response Analyzer
- Connect the specimen to a frequency response or network analyzer and configure a logarithmic sweep over the defined span.
- Select a sweep rate slow enough, with sufficient dwell or settle time at each frequency, so that transient ringing does not distort the measured magnitude, especially near high-Q resonances.
- Run the sweep and capture the magnitude trace directly as a Bode plot.
- Use marker and cursor functions to extract cutoff frequencies, peak values, and bandwidth automatically.
- Repeat the sweep at least twice to confirm repeatability before accepting the result.
Step 4: Broadband Excitation with FFT Analysis
- Excite the specimen with periodic chirp, stepped-sine, or random noise covering the full frequency band simultaneously.
- Capture input and output signals simultaneously with a data acquisition system at a sampling rate at least 10 times the highest frequency of interest.
- Compute the frequency response function using the H1 estimator (cross-spectrum of input and output divided by the input auto-spectrum), consistent with the principles of ISO 18431-2.
- Apply averaging over multiple records and verify coherence above approximately 0.9 across the band to confirm valid measurements.
- Extract amplitude-frequency parameters from the averaged magnitude curve.
Step 5: Vibration-Based Frequency Response Testing for Mechanical Specimens
- Bolt or bond the specimen to an electrodynamic shaker table using a fixture whose first resonance lies well above the test range.
- Mount a control accelerometer at the excitation point and response accelerometers at critical locations per ISO 16063-21 and GB/T 13823.
- Perform a low-level sine sweep in accordance with GB/T 2423.10, maintaining constant acceleration amplitude at the control point.
- Record the response acceleration at each frequency and compute transmissibility, the ratio of response to control acceleration.
- Identify resonant frequencies, amplification factors, and half-power bandwidths from the transmissibility curve, then verify structural integrity with a post-test inspection.
Step 6: Data Processing and Reporting
- Convert all ratios to decibel form and plot magnitude versus logarithmic frequency for each measurement channel.
- Apply mild smoothing or curve fitting only where justified, and never across sharp resonant peaks.
- Evaluate measurement uncertainty from instrument accuracy, noise floor, loading effects, and repeatability data.
- Compile a report containing the test setup diagram, instrument list and calibration status, environmental conditions, raw data tables, the amplitude-frequency curve, extracted parameters, and conformity conclusions against the applicable specification.
Applications
Amplitude-frequency characteristic experiments support design verification, product qualification, and research across many industries. Typical applications include:
- Verification of filter and amplifier designs against target frequency response specifications in electronics manufacturing.
- Calibration and selection of accelerometers and microphones in accordance with ISO 16063, IEC 61094, and IEC 61672.
- Resonance surveys and vibration qualification of aerospace, automotive, and railway hardware per GB/T 2423.10 and related EN standards.
- Audio and electroacoustic performance assessment of loudspeakers and sound systems following the IEC 60268 series.
- Control loop analysis, where the magnitude Bode plot supports stability margin assessment.
- Structural dynamics and modal analysis, where measured frequency response functions feed modal parameter extraction.
- University laboratory instruction in circuit theory, automatic control, and vibration engineering courses.
- Independent verification testing performed by accredited third-party laboratories for product certification purposes.
FAQ
What is the amplitude-frequency characteristic of a system?
It is the magnitude of the frequency response function, showing how much the system amplifies or attenuates a sinusoidal input at each frequency. It is usually presented as a gain curve in decibels versus logarithmic frequency.
How does it differ from the phase-frequency characteristic?
The amplitude-frequency characteristic describes only the magnitude ratio between output and input, while the phase-frequency characteristic describes the phase shift between them. Together they form the complete frequency response, but many practical pass/fail criteria rely on the amplitude curve alone.
Why is the frequency axis usually logarithmic?
Because system behavior spans several decades of frequency, logarithmic spacing distributes measurement points efficiently, matches the logarithmic behavior of filters and resonant systems, and makes roll-off slopes appear as straight lines.
What does the -3 dB cutoff frequency mean?
It is the frequency at which the output amplitude has fallen to 70.7 percent of the passband reference value, corresponding to a power ratio of one half. The band between the two -3 dB points defines the conventional bandwidth.
What instruments are required for the experiment?
A typical setup includes a function generator or frequency response analyzer, an oscilloscope or true-RMS voltmeter, a dynamic signal analyzer or data acquisition system, and, for mechanical specimens, an electrodynamic shaker with a controller and calibrated accelerometers.
What are the main sources of measurement error?
Common errors include insufficient signal-to-noise ratio, input amplitude drift during point-by-point testing, sweep rates that are too fast near resonances, loading effects from measurement instruments, cable and fixture resonances, and operation outside the specimen's linear range.
Which standards govern this type of testing?
Frequently applied documents include ISO 16063 and ISO 7626 for vibration measurements and calibration, IEC 61672 and the IEC 60268 series for electroacoustic equipment, GB/T 13823 for sensor calibration methods, GB/T 2423.10 for sinusoidal vibration testing, and IEC 61010-1 for measurement equipment safety. Specific product families may reference additional EN, UL, ASTM, or JIS standards.