Chapter 21: Optoelectronic Devices in Wireless Systems
Source: Hunsperger, sixth edition (2009), Problems 21.1–21.8, printed pages 464–465.
Problem 21.1 — Overall microwave-link power gain
Working. Multiply the two conversion slopes and optical transmission \(T=1/2.5\):
With the specified equal resistances, \(G_P=G_I^2R_{\rm out}/R_{\rm in}=144\).
Answer. Power gain is 144, or \(10\log_{10}(144)=21.5836\) dB.
Check. Current gain is 12, not the power gain. The units of the two electro-optic slopes cancel only after optical transmission is included.
Problem 21.2 — Bandwidth under increased laser power
Working. If the quoted bandwidth is limited by the laser’s relaxation frequency, use the usual approximation \(f_R\propto\sqrt P\) at a fixed device/operating regime:
Answer. Approximately 56.6 GHz under that specific relaxation-limited assumption.
Check. Optical power alone does not determine whole-link bandwidth. An RC-, receiver-, package-, or transit-limited 40 GHz link could remain near 40 GHz after increasing power.
Problem 21.3 — Materials for an OMMIC
Working. III–V direct-gap alloys support optical emission and detection, while high carrier mobility permits microwave electronic devices. AlGaAs layers are compatible with GaAs; appropriate InGaAsP compositions can be lattice matched to InP.
Answer. GaAs is the natural substrate for GaAs/AlGaAs devices, and InP for lattice-matched InGaAsP devices. Material composition sets optical wavelength and confinement.
Check. The acronym describes integrating microwave and optoelectronic functions; substrate choice still requires compatible lattice constants, bandgaps, and processing.
Problem 21.4 — Unequal-resistance link gain
Working. For sinusoidal currents, the same peak/RMS conversion appears at each port and cancels:
Answer. \(G_{\rm dB}=10\log_{10}(450)=26.5321\) dB.
Check. Using \(20\log_{10}(30)\) alone neglects the resistance ratio and overestimates power gain by 3.0103 dB.
Problem 21.5 — Four enabling improvements
Working. In the book’s historical interval, low-loss fiber extended reach; stable narrow-linewidth semiconductor lasers enabled dense channel allocation; high-speed modulators/detectors raised per-channel rate; and optical amplifiers restored many channels together without electronic regeneration at every repeater.
Answer. Those four developments form a consistent explanation for modern lightwave telecom in the edition’s context.
Check. Explain the role of each improvement rather than listing four kinds of components with no connection to capacity, reach, or practical deployment.
Problem 21.6 — GaAs and InP substrate advantages
Working. The substrate supports compatible epitaxial optical and microwave device layers. High electron mobility enables fast electronic devices; direct-gap active layers provide gain and detection; semi-insulating substrates can reduce parasitic coupling between microwave structures.
Answer. The platform can combine lasers, detectors, waveguides, and microwave electronics with reduced interconnect and packaging length.
Check. The bare substrate need not perform every optical function. Alloy layers and doping provide the required bandgap, index, and carrier profiles.
Problem 21.7 — Gain from the two peak currents
Working. With 10 mA input, 15 mA output, and equal 50 ohm resistances,
Answer. Approximately 3.522 dB.
Check. Use either peak currents at both ports or RMS at both ports. Mixing them creates a factor of two in power.
Problem 21.8 — Double the receiver resistance
Working. Keeping the stated current amplitudes unchanged, increase \(R_{\rm out}/R_{\rm in}\) from one to two:
Answer. Approximately 6.532 dB under the unchanged-current assumption, a 3.0103 dB increase.
Check. A real receiver load change may also change current and bandwidth. The arithmetic result uses the idealized fixed-current comparison requested by the question.