Chapter 1: Introduction

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) = Vp sin(wt + Φ)

– Vp : peak value

– w: angular velocity

– Φ: phase angle

• Can modulate by varying:

– Vp : 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 P2 / P1

• Voltage Gain: dB = 20 log V2 / V1

• dB using a 1W reference: 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(RL) = 20 log V / V0dBm

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: Pn = 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

• Pn = (en / 2)2 / R = KT ∆f

• Noise Voltage (rms value):

en = 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 = Ps / Pn

– Ps: Signal Power

– Pn: NoisePower

• Typically in dB: SNR(dB) = 10 log (Ps / Pn)

Noise Figure (NF)

• Measure of a device degradation to SNR

• The lower, the better

• Formula: NF = 10 log SNRin / SNRout

– SNRin : SNR at device’s input

– SNRout : SNR at device’s output

• Noise Ratio: NR = SNRin / SNRout

• Useful Relationship: SNRout = SNRin – 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: 3rd 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 (sint + 1/3 sin 3t); (c) the addition of the first, third, and fifth harmonics (sin t + 1/3 sin 3t + 1/5 sin 5t).

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

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

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.