Electrical spectrum analyzer (ESA, RF spectrum analyzer)

An electrical spectrum analyzer (ESA), also called an RF or microwave spectrum analyzer, measures how the power of an electrical signal is distributed over frequency. Each trace point is the power, usually in dBm, passing a filter of width equal to the resolution bandwidth (RBW) centered at that frequency. Bench instruments reach from hertz or kilohertz to tens of gigahertz, with RBW settings from about 1 Hz to a few megahertz. In a photonics lab the ESA usually sits after a fast photodiode, displaying the spectrum of the optical intensity and of beat notes between optical fields.

Swept and FFT analyzers

A swept superheterodyne analyzer mixes the input with a tunable local oscillator so that each input frequency in turn is converted to a fixed intermediate frequency, filters it there with the RBW filter, and detects the power. Its span can be very wide, but a narrow RBW forces a slow sweep, since the minimum sweep time scales as span/RBW². An FFT or real-time analyzer digitizes a band of the input and computes the spectrum from time records, which is faster at narrow RBW over modest spans and captures transient or intermittent signals that a sweep would miss.

Noise floor and RBW

The displayed average noise level is the thermal noise of a matched 50 Ω input, −174 dBm/Hz at 290 K, raised by the analyzer's noise figure and scaled by the RBW:

$$N = -174 + \mathrm{NF} + 10\log_{10}(\mathrm{RBW}/\mathrm{Hz})$$

in dBm. With a 15 dB noise figure the floor is −159 dBm/Hz, or −109 dBm at 100 kHz RBW. A narrow line reads the same at any RBW while broadband noise scales with it, so a narrower RBW lifts a weak tone out of the noise floor at the cost of sweep time. Noise readings are converted to a density by subtracting $10\log_{10}(\mathrm{RBW}/\mathrm{Hz})$, using the filter's noise bandwidth; the analyzer's noise marker does this and also corrects the 2.51 dB underreading that log-scale averaging gives for Gaussian noise.

Measurements in photonics

• Intensity noise. The relative intensity noise spectrum of a laser, including the peak at the relaxation oscillation frequency, typically a few gigahertz to above 10 GHz in a semiconductor laser.
• Beat notes. Two lasers combined on a photodiode give a tone at their difference frequency whose width is their combined linewidth: heterodyne detection read on an ESA.
• Linewidth. In the delayed self-heterodyne method the laser beats with a delayed, frequency-shifted copy of itself, and the beat note near the acousto-optic shift frequency, viewed at kilohertz-scale RBW, gives the linewidth.
• Pulse trains and mode spacing. A mode-locked laser produces a comb of lines at its repetition rate and harmonics, and the noise skirts of these lines measure timing jitter; a multimode laser shows a beat at its longitudinal mode spacing.

Converting a reading to RIN

RIN is the noise power spectral density divided by the average electrical power of the detected signal, both referred to the same point. Suppose a photodiode delivers an average photocurrent of 2 mA into the analyzer's 50 Ω input. The average electrical power is $I^2R = 0.2$ mW, or −7.0 dBm; it is computed from the photocurrent measured on a meter, because the ESA input is usually AC-coupled and does not display it. If the noise marker reads −95 dBm in a 100 kHz RBW at some frequency, the density there is

$$-95 - 10\log_{10}(10^5) = -145\ \text{dBm/Hz},$$

and the RIN is $-145 - (-7.0) = -138$ dB/Hz. The analyzer floor (−159 dBm/Hz at 15 dB noise figure) lies 14 dB below the reading, and the shot noise of 2 mA, $2qIR$ = −165 dBm/Hz, corresponds to a RIN of −158 dB/Hz, so neither corrupts the result. The full procedure, including calibrating the detector's frequency response, is in Relative Intensity Noise Measurement of Semiconductor Lasers.

ESA, OSA and network analyzer

An optical spectrum analyzer resolves the optical field itself; a grating OSA at 0.02 nm resolution has a bandwidth of 2.50 GHz at 1550 nm, about $2.5 \times 10^9$ times wider than a 1 Hz ESA filter. A network analyzer differs again: it supplies its own swept stimulus and measures the ratio of response to stimulus, including phase, whereas the ESA only receives.

Pitfalls

Overdriving the input mixer generates harmonics and intermodulation products that look like real spectral lines; switching in more input attenuation leaves a real line's displayed level unchanged but changes the level of products generated inside the analyzer. The photodiode and any amplifier have their own frequency response, which shapes the displayed spectrum unless calibrated out.

Common questions

What is the difference between an ESA and an OSA?

The ESA measures the spectrum of an electrical signal, with hertz-level resolution up to tens of gigahertz; the OSA measures the optical spectrum, spanning hundreds of nanometers but with gigahertz-scale resolution.

Can an ESA measure a laser's linewidth?

Only through a beat note, against a second laser or against a delayed copy of the laser itself; directly on a photodiode, a single-frequency laser's linewidth does not appear in the intensity spectrum.

References: D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998); P. Horowitz and W. Hill, The Art of Electronics, 3rd ed. (Cambridge University Press, 2015); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012).