6041EE Advanced Electronics Coursework Part 2: FM Radio Transmission Design Model Answer (Coventry University, PSB Academy) Singapore

For information and reference only – not to be submitted as your own work. This extract shows how a Coventry University 6041EE Advanced Electronics Coursework Part 2 FM radio transmission design can be worked through, as studied at PSB Academy Singapore. It uses one illustrative data set, not your assigned one.

For the question background, see the sister Coventry University PSB Academy brief, the 6032EE power systems coursework question; a dedicated 6041EE question page will be linked here when it is live. For the marking logic, read our guide to what markers want in 6041EE FM transmitter design.

Illustrative data set

All values below are illustrative values – replace with your own assigned data. The method is what matters; every number must be recomputed for your own channel, distance and transistor table.

System explanation

The transmitter up-converts the audio signal to the FM broadcast band. An FM modulator produces a 10.70 MHz intermediate frequency (IF); a mixer and a local oscillator (LO) at 87.80 MHz then create the sum product at 98.50 MHz. The first bandpass filter (BPF) cleans the mixer output, the input matching network (IMN) presents the correct source impedance to the RF power amplifier (PA), and the output matching network (OMN) delivers power to the second BPF, the quarter-wave transformer and the antenna.

Unwanted mixer products matter. Besides the wanted 98.50 MHz, the mixer emits LO leakage at 87.80 MHz, the difference product at 77.10 MHz and IF feedthrough at 10.70 MHz. Carson’s rule gives an occupied bandwidth of 2(75 + 15) = 180 kHz for 75 kHz deviation and 15 kHz audio, which fits the 200 kHz channel spacing. A comparable worked radar-chain explanation appears in our ENG330 radar system applications sample.

Bandpass filter design

I chose a 3rd-order Butterworth bandpass with a 6.00 MHz bandwidth, because it is flat in band and needs no tuning of ripple. The fractional bandwidth is FBW = 6.00 / 98.50 = 0.0609, so the loaded Q is 16.42. Low-pass prototype elements [2] are g1 = 1.00, g2 = 2.00, g3 = 1.00, with ω0 = 2π × 98.50 MHz = 618.89 Mrad/s and Z0 = 50.00 Ω.

For the series resonators: L = g Z0 / (ω0 FBW) and C = FBW / (ω0 g Z0). For the shunt resonator: C = g / (ω0 FBW Z0) and L = FBW Z0 / (ω0 g).

Rejection follows 10 log10(1 + x^6) with x = (f/f0 − f0/f)/FBW. This gives 34.68 dB at the 87.80 MHz LO, 54.58 dB at 77.10 MHz and 31.83 dB at 109.20 MHz. Using the standard estimate IL ≈ 4.343 Σg / (FBW × Qu), an inductor unloaded Q of 150 gives an insertion loss of 1.90 dB per filter. I assume that value in the power budget.

Transistor stability and the simultaneous conjugate match

First test stability. With D = S11S22 − S12S21, |D| = 0.07. The Rollett factor is K = (1 − |S11|² − |S22|² + |D|²) / (2|S12S21|) = 1.81. Since K > 1 and |D| < 1, the transistor is unconditionally stable at 98.50 MHz and a simultaneous conjugate match exists. Always repeat this check at other frequencies [4]; a device that is stable at 98.50 MHz can still oscillate elsewhere.

Using B1 = 1 + |S11|² − |S22|² − |D|² = 1.14 and C1 = S11 − D S22*, the source reflection coefficient is Γms = [B1 − √(B1² − 4|C1|²)] / (2C1) = 0.66 at 150.57°. The same method with B2 = 0.85 gives Γml = 0.55 at 36.14°. Following [1], the maximum available gain is MAG = |S21/S12| (K − √(K² − 1)) = 201.04, or 23.03 dB.

Input matching network (Smith chart method)

The IMN must make the transistor see Zs = Z0(1 + Γms)/(1 − Γms) = 11.05 + j12.53 Ω, which normalises to zs = 0.22 + j0.25. Normalising by 50 Ω is the step students most often forget. On the Smith chart, the required admittance is ys = 1.98 − j2.24, so a shunt element at the 50 Ω side followed by a series element at the transistor does the job.

For R < Z0 the L-network needs a series reactance Xs = √(R(Z0 − R)) − X. With R = 11.05 Ω and X = −12.53 Ω (conjugate taken because the network is seen from the transistor), Xs = 20.75 + 12.53 = 33.27 Ω, giving a series inductor L = 33.27 / ω0 = 53.76 nH. The shunt susceptance B = 0.0376 S then gives C = B / ω0 = 60.68 pF. Recomputing the cascade returns 11.05 + j12.53 Ω, confirming the match.

RF power amplifier design

I selected Class A because the S-parameters are small-signal data valid only around the stated bias. FM is constant-envelope, so a later redesign to Class AB or C for efficiency is defensible, but then large-signal data would be needed. At Vce = 6.00 V and Ic = 70.00 mA the ideal Class A maximum output is 0.5 × 6.00 × 0.07 = 0.21 W (23.22 dBm).

Bias design with Vcc = 7.50 V, β = 100.00 assumed: VE = 1.50 V gives RE = 1.50 / 0.07 = 21.43 Ω. Then VB = 2.20 V, IB = 0.70 mA, and a divider current of 10 IB = 7.00 mA gives R2 = 314.29 Ω and R1 = 688.31 Ω. Add an RF choke at the collector and DC-blocking capacitors at both ports. Operating gain with perfect matching equals the MAG of 23.03 dB; I derate by 1.00 dB to 22.03 dB for component tolerance.

Output matching network

The OMN must present Zl = 84.09 + j79.24 Ω (zl = 1.68 + j1.58) to the collector. Here R > Z0, so the first element is a shunt one. The conjugate-adjusted solution is a shunt capacitor of 5.42 pF at the collector followed by a series inductor of 119.16 nH towards the 50 Ω line. Recomputing gives 84.09 + j79.25 Ω, which agrees to rounding.

Quarter-wave antenna transformer

Assume the antenna feed presents 25.00 Ω (illustrative). A quarter-wave section matching 50.00 Ω to 25.00 Ω needs Z0T = √(Z1 Z2) = √(50.00 × 25.00) = 35.36 Ω. In free space λ = c/f = 3.04 m, so λ/4 = 0.76 m. With a velocity factor of 0.66 for the line, the physical length is 0.76 × 0.66 = 0.50 m. The usable bandwidth of one quarter-wave section is far wider than the 200 kHz channel.

Power budget, mixer output to antenna

I assume a mixer output of 0.00 dBm. Each stage adds its gain or loss in dB.

The transmit power at the antenna terminals is therefore Pt = 17.43 dBm (55.34 mW). The PA output of 19.83 dBm sits 3.39 dB below the 23.22 dBm Class A limit, so the stage stays linear.

Free-space path loss and receiver check

FSPL = 20 log10(d km) + 20 log10(f MHz) + 32.44 = 33.98 + 39.87 + 32.44 = 106.29 dB, as given in ITU-R P.525 [3]. Received power is Pr = Pt + Gt + Gr − FSPL − blockage = 17.43 + 0.50 + 1.00 − 106.29 − 10.00 = −97.36 dBm.

This is 17.36 dB below the −80.00 dBm sensitivity, so the signal is not sufficient. The remedies are compared below. Gt and Gr are fixed by the assigned ranges, so the levers are power, blockage and path length.

A 1.21 dB margin is thin. A 25.00 km repeater hop reduces FSPL to 100.27 dB, a saving of 6.02 dB per hop. My recommendation is a 30.00 dBm final stage plus a taller antenna as the minimum, with a repeater if a 10 dB fade margin is demanded.

Final circuit component table

Round to the nearest preferred values only after a sensitivity check; a 5.42 pF capacitor with ±5% tolerance moves the match noticeably. For real parts, choose an RF transistor whose datasheet publishes S-parameters at your Vce and Ic, with a transition frequency well above 100 MHz and an output rating above the 19.83 dBm demanded here. I have not named a part here, because the brief requires S-parameters from the actual datasheet.

Fading, stray parasitics and PCB layout

FM signals suffer multipath fading when reflected paths from buildings arrive out of phase. A vehicle at 100.00 km/h produces a maximum Doppler shift of v f / c = 9.13 Hz, so fades are slow compared with 15 kHz audio but can still produce brief dropouts. Building blockage is shadowing, treated here as the 10.00 dB loss. Diversity reception and a fade margin address both.

On the PCB, trace inductance of roughly 1 nH per millimetre (a rule of thumb) means 5 mm of track adds about 5 nH to the 53.76 nH IMN inductor. Pad capacitance of 0.2 pF is about 4% of the 5.42 pF OMN capacitor. Keep tracks short, add a solid ground plane, place decoupling at the PA, and separate input from output to protect the stability found earlier. Our EE2024 interfacing sample shows a similar approach to documenting hardware assumptions.

State every assumption: mixer output level, filter Q, β, antenna impedance and velocity factor. Markers award marks for justified assumptions, not silent ones.

Stuck on your own data set? Our telecommunication assignment help team provides model answers and academic support, and you can read student reviews first. Related subject coverage sits under electrical and electronic engineering assignment help.

About the expert

Wei Zhao holds a Master’s in Electrical Engineering from the National University of Singapore, with specialisms in power systems, signal processing, control systems and telecommunications. Wei has 7 years as an academic writer, including 3 years with Singapore Assignment Help.

References

[1] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, 2012.

[2] R. Ludwig and P. Bretchko, RF Circuit Design: Theory and Applications. Upper Saddle River, NJ, USA: Prentice Hall, 2000.

[3] International Telecommunication Union, “Calculation of free-space attenuation,” ITU-R Recommendation P.525-4, Aug. 2019.

[4] G. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design, 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall, 1997.