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Optical and Electrical Bandwidth of LED

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We now discuss specifically the electrical bandwidth. We had defined the transfer function H(jω), as the
the ratio of the carrier density due to the injection current at a frequency ω to that at zero frequency. Now, the
carrier density is proportional to the number of photons generated and hence, H(jω), with magnitude
1/ඥ1 + ω௠
ଶτ௖
ଶ, can also be written as Poptical (ω)/Poptical (0 ), and hence indicates the optical transfer
function and the corresponding estimated bandwidth is the optical bandwidth. We would now calculate
the electrical bandwidth of the driver electronics that would support a given 3 dB optical bandwidth for
an LED.

NPTEL-Fiber Optic Communication Technology- Lecture 14 Page 2
Consider the LI characteristics is shown in slide 27, which is a straight line passing through the
origin. During modulation, the current is typically biased at a specific value- indicated as the bias current,
Ib and its value swings between Imax to I min during modulation. Typically, this is implemented in an
electronic circuit using a bias tee – which is a combination of inductor and capacitor. The AC component
that is to be modulated passes through a coupling capacitance and a DC - which is the bias current, is fed
through the inductance. The combination of this would drive the LED or even a laser diode.
Let us take an example of τc= 50 nanoseconds. Now, 3 dB optical bandwidth calculated from the
expression, √3/2πτ௖

is 5.5 MHz. It means that you can modulate the LED as fast as 5.5 MHz because of
the recombination time of 50 ns. The optical power is proportional to the electrical drive current.
The electrical 3 dB bandwidth is defined as P electrical (ω)/P electrical (0). This can be calculated from the
electrical transfer function. This electrical power P electrical drawn in the circuit is proportional to the square
of the current while the optical power generated is, P optical is proportional to current.
Thus, the electrical transfer function must be the square of the optical transfer function and is given as,
|H(jω|
ଶ = ቎

ටଵାఠ೘
మఛ೎

=

ଵାఠ೘
మఛ೎

.

The 3-dB electrical bandwidth is given as, f௘௟௘௖௧௥௜௖௔௟
ଷௗ஻ =

ଶగఛ೎
so, f௢௣௧௜௖௔௟
ଷௗ஻ =√3f௘௟௘௖௧௥௜௖௔௟
ଷௗ஻
.

For τc
= 50 ns, f௘௟௘௖௧௥௜௖௔௟

ଷௗ஻ =3.2 MHz, so the drive circuit need to support the optical bandwidth

of f௢௣௧௜௖௔௟
ଷௗ஻ = 5.5 MHz. It needs to have a bandwidth of only 3.2 MHz.

NPTEL-Fiber Optic Communication Technology- Lecture 14 Page 3
It has to be taken care while measuring the bandwidth of an LED that, the bandwidth of the photodiode
(measurement system) should be larger than the expected bandwidth of the LED. Also, it should be
ensured that the parasitic capacitance due to the junction capacitance and the cable capacitance should not
limit the measurement bandwidth.