Network analyzer

A network analyzer drives a device with a sine wave of known amplitude, sweeps its frequency, and measures the waves reflected from and transmitted through the device. A vector network analyzer (VNA) records both magnitude and phase; a scalar analyzer records magnitude only. The results are the scattering parameters: $S_{11}$, the reflection at port 1, and $S_{21}$, the transmission from port 1 to port 2, each a complex ratio of outgoing to incoming wave amplitude referred to a 50 Ω system. Instruments used for photonic devices typically span from tens of megahertz to 67 GHz or 110 GHz, with frequency extenders above that, and reach a dynamic range above 100 dB at narrow receiver bandwidths. In photonics labs the VNA is the standard instrument for the modulation bandwidth of lasers, modulators and photodiodes.

What the S-parameters give

Because S-parameters are amplitude ratios, they are plotted as $20\log_{10}|S|$ in dB (see decibel). A reflection of $S_{11} = -20$ dB is $|\Gamma| = 0.1$, 1% of the incident power reflected, a voltage standing-wave ratio of 1.22; $-10$ dB is 10% reflected and a VSWR of 1.92. The magnitude of $S_{21}$ is the gain or insertion loss of the path. Its phase gives the group delay,

$$\tau_g = -\frac{d\phi}{d\omega},$$

so a phase that falls by 360° over 1 GHz corresponds to a delay of 1 ns. Flat group delay across the band matters for modulator electrodes and drivers.

Calibration

The raw measurement includes the analyzer's internal couplers, cables and connectors. Calibration measures known standards and solves for the systematic error terms, moving the reference planes to the device's own ports. The common coaxial method is SOLT (short, open, load, thru), which for a full two-port calibration determines a 12-term error model; TRL (thru, reflect, line) is preferred on wafer and in fixtures where a good broadband load is hard to make. Anything left between the calibration plane and the device, such as an RF probe, a bias tee or a package trace, is removed afterwards by de-embedding its measured S-parameters. A calibration holds only for the cable positions, connector torque and temperature at which it was made.

The receiver's IF bandwidth plays the role that resolution bandwidth plays in a spectrum analyzer: narrowing it from 10 kHz to 100 Hz lowers the noise floor by 20 dB at the cost of a slower sweep.

Lightwave component analyzers

For optoelectronic devices one port is optical. A lightwave component analyzer combines a VNA with a calibrated reference modulator and a calibrated reference receiver, so that it can measure E/O devices (a laser or modulator driven electrically, read optically) and O/E devices (a photodiode driven by modulated light, read electrically). The O/E response is usually reported in dB relative to 1 A/W on a $20\log_{10}$ scale, so a photodiode with a low-frequency responsivity of 0.8 A/W reads $-1.9$ dB. The reference modulator and receiver are themselves calibrated, usually by optical heterodyning of two lasers; an uncalibrated modulator cannot be used to characterize an uncalibrated detector. The procedures are given in How to measure photodetector bandwidth and How to measure electro-optic modulator bandwidth.

Electrical and optical 3 dB bandwidth

A photodiode's current is proportional to optical power, and the VNA reads electrical power, proportional to the square of the current. The trace therefore falls by 3 dB when the modulation amplitude has fallen to $1/\sqrt{2}$ of its low-frequency value; this is the electrical 3 dB bandwidth, the one normally quoted for photodiodes and Mach-Zehnder modulators. An "optical 3 dB" bandwidth, where the modulation amplitude has halved, lies at the 6 dB point of the same trace and is a higher frequency. A bandwidth figure is comparable with another only when both use the same convention.

Optical vector analyzers

An optical vector analyzer applies the same idea to passive optical components. A tunable laser sweeps across the band, and a polarization-diverse interferometer, related to optical frequency-domain reflectometry, measures the component's complex transfer function. From the full polarization response it computes insertion loss, group delay, chromatic dispersion, polarization-mode dispersion and polarization-dependent loss against wavelength, for filters, gratings and photonic integrated circuits.

Pitfalls

Drive power that is too high compresses the response of a modulator or amplifier and flattens the measured curve; the check is that the normalized response does not change when the drive is lowered a few dB. On O/E measurements the received RF power falls with the square of the optical power, so a weak optical signal places the high-frequency response near the noise floor. Bias is part of the result: photodiode bandwidth depends on reverse bias and photocurrent, laser bandwidth on drive current, and both are reported with the bandwidth.

Common questions

What is the difference between a VNA and a spectrum analyzer?

A VNA supplies its own swept stimulus and measures the ratio of response to stimulus, including phase. A spectrum analyzer only receives: it measures the power spectrum of whatever signal is applied and has no knowledge of a stimulus.

What do S11 and S21 mean?

$S_{11}$ is the wave reflected at port 1 divided by the wave incident on port 1, with port 2 terminated in a matched load. $S_{21}$ is the wave leaving port 2 divided by the wave incident on port 1: the forward transmission.

References: D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, 2012); D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).