EET-223: RF Communication Circuits
Walter Lara

Introduction
• Electronic communication involves transmission over medium from source to destination
• Information can contain voice, picture, sensor output, or any data.
• Intelligence signal or simply “intelligence”– contains information to transmit
• Intelligence is at frequencies too low to transmit
(e.g. voice 20Hz – 3 KHz) - would require huge antennas

Introduction – Cont’d
• Multiple intelligence signals have the same frequency (e.g. voice) - would result on interference if transmitted simultaneously
• Modulation – process of putting intelligence signal onto high-frequency carrier for transmission
• Demodulation – process of extracting the intelligence from a transmitted signal

Introduction – Cont’d
• Carrier signal is a sinusoid:
– v(t) = V p
– V p sin(wt + Φ)
: peak value
– w: angular velocity
– Φ: phase angle
• Can modulate by varying:
– V p
: Amplitude Modulation (AM)
– w: Frequency Modulation (FM)
– Φ: Phase Modulation (PM)

Introduction – Cont’d
• RF Spectrum divided into ranges. Example:
– MF (300 KHz – 3 MHz): AM Radio
– VHF (30-300 MHz): FM Radio, some TV, some cellphones
– UHF (300MHz – 3 GHz): TV, cellphones, WiFi, microwaves
• See Table 1-1 for complete details

Figure 1-1 A communication system block diagram.

The Decibels (dB) in Communications
• Used to specify measured and calculated values of voltage, power and gain
• Power Gain: dB = 10 log P
2
• Voltage Gain: dB = 20 log V
2
• dB using a 1W reference:
/ P
1
/ V
1 dBW = 10 log P / 1 W
• dB using a 1mW reference: dBm = 10 log P / 1 mW
• dB using a 1mW reference with respect to a load: dBm(R
L
) = 20 log V / V
0dBm

Noise
• Any undesired voltages/currents that appear in a signal
• Often very small (~uV)
• Can be introduced by the transmitting medium
(external noise):
– human-made (e.g. sparks, lights, electric motors)
– atmosphere (e.g. lightning)
– space (e.g. sun)
• Can be introduced by the receiver (internal noise):
– physical properties of electronic components

Figure 1-2 Noise effect on a receiver s first and second amplifier stages.

Thermal Noise
• Aka Johnson or White Noise
• Random voltage fluctuations across a circuit component caused by random movement of electrons due to heat
• Contains “all” frequencies (all colors = white)
• Power from Thermal Noise: P n
= KT ∆f
– K = 1.38 x 10 -23 J/K (Boltzman’s Constant)
– T: resistor temperature, in Kelvins
– ∆f: bandwidth of system

Figure 1-3 Resistance noise generator.

Thermal Noise – Cont’d
• P n
= ( e n
/ 2) 2 / R = KT ∆f
• Noise Voltage (rms value): e n
= 𝟒𝑲𝑻∆𝒇𝑹
• Textbook assumes room temperature is
17C = 290.15 K, so 𝟒𝑲𝑻 = 1.6 x 10 -20 J

Other Noise Sources
• Shot Noise – caused by the fact that electrons are discrete particles and take their own random paths
• Transit-Time Noise – occurs at high frequencies near the device cutoff frequency
• Excess Noise – occurs at low frequencies
(<1 KHz), caused by crystal surface defects

Figure 1-4 Device noise versus frequency.

Signal-to-Noise Ratio (S/R or SNR)
• Very important & common measure
• The higher, the better
• Formula: SNR = P s
– P s
: Signal Power
– P n
: NoisePower
/ P n
• Typically in dB: SNR(dB) = 10 log (P s
/ P n
)

Noise Figure (NF)
• Measure of a device degradation to SNR
• The lower, the better
• Formula: NF = 10 log SNR
– SNR in
– SNR out in
: SNR at device’s input
/ SNR
: SNR at device’s output out
• Noise Ratio: NR = SNR in
• Useful Relationship:
/ SNR out
SNR out
= SNR in
– NF (all in dB)

Information & Bandwidth
• Amount of information transmitted in a given time is limited by noise & bandwidth
• Harley’s Law: information α bandwidth x time of transmission
• In USA, bandwidth is regulated by FCC
– AM Radio: 30 KHz
– FM Radio: 200 KHz
– TV: 6 MHz

Fourier Analysis
• Any signal can be expressed as the sum of pure sinusoids.
• See Table 1-4 for selected waveforms
• For a square wave: v = 4V/π (sin wt + 1/3 sin 3wt + 1/5 sin 5wt + …)
– sin wt : fundamental frequency
– 1/3 sin 3wt: 3 rd harmonic
– 1/5 sin 5wt: 5th harmonic
• The more bandwidth, the better representation

Figure 1-9 (a) Fundamental frequency (sin
 t ); (b) the addition of the first and third harmonics (sin
 t + 1/3 sin 3
 t ); (c) the addition of the first, third, and fifth harmonics (sin
 t + 1/3 sin 3
 t + 1/5 sin 5
 t ).

Figure 1-9 (continued) ( a) Fundamental frequency (sin
 t ); (b) the addition of the first and third harmonics (sin
 t + 1/3 sin 3
 t ); (c) the addition of the first, third, and fifth harmonics (sin
 t + 1/3 sin 3
 t + 1/5 sin 5
 t ).

Figure 1-9 (continued) ( a) Fundamental frequency (sin
 t ); (b) the addition of the first and third harmonics (sin
 t + 1/3 sin 3
 t ); (c) the addition of the first, third, and fifth harmonics (sin
 t + 1/3 sin 3
 t + 1/5 sin 5
 t ).

Figure1-10 Square waves containing: (a) 13 harmonics; (b) 51 harmonics.

Figure1-10 (continued) Square waves containing: (a) 13 harmonics; (b) 51 harmonics.

Fast Fourier Transform (FFT)
• Signal processing technique that converts time-varying signals to frequency components using samples
• Allows Fourier analysis when using oscilloscopes and spectrum analyzers

Figure 1-11 (a) A 1-kHz sinusoid and its FFT representation; (b) a 2-kHz sinusoid and its FFT representation.

Figure 1-11 (continued) (a) A 1-kHz sinusoid and its FFT representation; (b) a 2-kHz sinusoid and its FFT representation.

Figure 1-12 A 1-kHz square wave and its FFT representation.

Figure 1-13 (a) A low-pass filter simulating a bandwidth-limited communications channel; (b) the resulting time series and FFT waveforms after passing through the low-pass filter.