Microwave Circuits Review Part I

Index
1. Introduction
2. Wireless Communication Systems
   2.1. Modulation and Demodulation
   2.2. Receiver and Transmitter
   2.3. Spectral Efficiency and Power Efficiency
   2.4. Microwave Link Design
   2.5. Multipath Propagation
3. Transmission Lines
   3.1. Characteristics and Reflection Coefficient
   3.2. TL Frequency Response
   3.3. Planar Transmission Lines
   3.4. High-Frequency TL Effects
   3.5. Coupled Lines Theory
   3.6. Directional Couplers

1. Introduction

This review is mostly based on Northeastern University EECE7250 Microwave Circuits for Wireless Communications, Fall 2020 lecture notes by Professor Amir Farhat. The notes are based on the book Microwave and RF Design, A Systems Approach by Michael Steer. Most figures and text screenshots are directly taken from the notes.

 

2. Wireless Communication Systems

2.1. Modulation and Demodulation

A microwave system is generally described by a microwave link: the transmitter (Tx), receiver (Rx), and a channel. The channel is the medium of transmission.

To enable wireless transmission, the information signal must be translated upward in frequency by encoding it into a high-frequency radio wave through a modulation process in the Tx. The inverse process is employed in the Rx to extract the baseband information from the received modulated carrier. The latter must be translated downward in frequency back to baseband by demodulation. The circuit functional block performing the frequency translation is often referred to as a mixer, or a modulator/demodulator. Present-day Tx and Rx systems are based on the superheterodyne architecture:

Mixers require a second input: a local oscillator (LO) with a frequency equal to the amount of up/down frequency translation necessary.

Modulation Format

A sinusoidal carrier wave at a microwave frequency f_c is modulated by the baseband digital data through variation of one or more of the carrier wave attributes:

1) Amplitude: amplitude shift keying (ASK)/on-off keying (OOK)

2) Frequency: frequency shift keying (FSK)

3) Phase: phase shift keying (PSK)

4) Quadrature amplitude: amplitude + phase (QAM)

The distribution of signal power over frequency is of importance as it determines the bandwidth B(Hz) required from amplifiers/filters handling these signals.

Power Spectrum

The power spectrum S(f) of the various digital modulations has common features. The mathematical description is given by the function: sinc²(x) = (sinx/x)².

S(f) = E_bsinc²[π(f – f_c)T_b]

In all the above modulation schemes, the spectral efficiency R_b/B is the same: 1 b/s/Hz.

M-ary Modulation Schemes

M-ary modulation schemes are higher-order modulations that are more spectrally efficient in that they permit higher data rates (R_b) to be transmitted over a  given BW. However, there exists a fundamental tradeoff between spectral efficiency (R_b/B) and power efficiency (SNR)

M-PSK has M-phase states:

s_i(t) = A cos(ω_ct – φ_i), φi = (i/M)2π, i = 0, 1, …, M-1

= a_icosω_ct + b_isinω_ct, where a_i = Acosφ_i, b_i = Asinφ_i, A = √(a_i² + b_i²)

M-PSK can be represented by phasors with cartesian components I (in phase) and Q (quadrature phase) in constellation diagrams.

M-ary QAM is obtained by allowing the amplitudes of the I & Q components to be modulated in addition to phase:

si(t) = A_icos(ω_ct – φ_i) = a_icosω_ct + b_isinω_ct

All M-ary PSK & QAM modulations require 90° phase shifting to produce the I & Q components. Also, the QAM format of modulation entails amplitude scaling as well as phase shift.

Modulation Blocks: I-Q Modulators

Power Spectra for M-ary Modulations

M-PSK: symbol rate R_s = R_b/k (T_s = kT_b), energy/symbol E_s = kE_b, B = R_s = R_b/k.

M-FSK: M-superimposed (orthogonal) spectra of the simple FSK, B = (M+1)R_s = (M+1)R_b/k.

M-QAM: B = R_s = R_b/k.

Demodulation Blocks

In an R_x, demodulation is commonly done through multiplication by a replica of the received carrier wave. The technique is called synchronous (or coherent) detection. The carrier wave cosω_ct is locally regenerated in the R_x, i.e., recovered from the received RF signal.

For ASK and BPSK demodulation, the received signal is simply multiplied by cosω_ct and then filtered by a LPF with BW = R_b. The filtered signal contains full information of the original data s(t).

While for FSK, QPSK, and QAM demodulation, the received signal has to be multiplied by two cosine waves that differ in frequency or phase and then filtered by a LPF and further DSP to obtain the original data.

Specifically, in orthogonal FSK demodulation, Δf = R_b, hence the BW of LPF is R_b/2. In QPSK and QAM demodulation, BW of LPF is R_s/2.