# Bandwidth Terminology

There are many terms used to describe the bandwidth of a photodetector, but the two most common, “optical bandwidth” and “electrical bandwidth” can be confusing when making detector comparisons.

A photodetector is a converter of optical power (mW) to electrical current (mA). High-speed detectors are designed to perform the optical to electrical conversion extremely quickly so when a short pulse of light arrives, the detector produces an exact replica of the input as a current pulse at the output.

The “speed” of a detector, or how fast it responds, can be determined by applying an extremely short optical pulse to the input, and then measuring the current produced at the output. The current pulse is directed through a load resistor (usually 50Ω) in order to generate a voltage pulse that can be displayed and measured on an oscilloscope. The width of this voltage pulse at 50% of its peak amplitude is known as the pulsewidth, and is often quoted as the “speed” of the detector in the time-domain.

The bandwidth of a detector, however, is measured by its response in the frequency-domain. The frequency response can be determined from the impulse response by mathematically transforming it into the frequency domain (via Fourier Transform) and then squaring the result to yield electrical power as a function of frequency. Theelectrical bandwidth, or -3dBe of the detector is then defined as the frequency at which the electrical power spectrum drops to 50% (or -3 dB) of its value at DC.

What if you just looked at the spectrum of the impulse itself, without squaring it to get power? Since the output current, or voltage, is proportional to input optical power, the point at which the voltage spectrum falls to 50% of its DC value is known as the optical bandwidth, or -3dBo.

The relationship between optical and electrical spectra can be seen in the figure below. The electrical spectrum simply goes as the square of the optical spectrum, because power is proportional to the square of the voltage. On the log scale, this squared relationship appears as a factor of two difference in decibels (dB). Therefore, when the optical power spectrum has dropped to its -3dB point, the corresponding electrical power spectrum has dropped to its -6dB point at exactly the same frequency.

Simply stated:
Electrical bandwidth = -3 dB electrical
Optical bandwidth = -3 dB optical = -6 dB electrical

As a result, be sure you are comparing apples with apples, or in the case of detectors, electrons with electrons, or photons with photons. Note that in all cases, the optical bandwidth is greater than the electrical bandwidth, although the exact ratio depends on the shape of each detector’s frequency response.

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