Module Introduction
Purpose:
– This training module provides an overview of some basic concepts of
RF design.
Objectives:
– Understand the concept of power transfer to a load.
– Explain how impedance matching is achieved.
– Recognize a Smith Chart and how it is used for impedance matching.
– Understand the importance of maintaining linearity in a device.
– Identify the factors that influence the signal-to-noise ratio in a system.
Content:
– 16 pages
– 3 questions
Learning Time:
– 30 minutes
This training module will give you an overview of some basic concepts used
in RF design.
In this module, we briefly discuss various considerations to take into account
when creating wireless communication systems, such as how to achieve
maximum power transfer in your system, using impedance matching to
achieve maximum power, how maintaining linearity in a system helps
improves signal quality, and how to reduce unwanted noise in a system.
1
Power Transfer to a Load
Maximum power is transferred when the Load resistance (RL)
“matches” the Source resistance (RS)
RS
Reflection Coefficient, Γ, quantifies
the quality of the match where:
RL
Γ
= ZL - Zo = RL - RS
ZL + Zo
RL + RS
=
Vreflected
Vincident
RS and RL can be generalized to ZS and ZL
Radio communications depends on transmitted energy. Energy implies power. This
has important consequences in RF circuitry. The impedances of RF transmission
media, including free space and RF circuitry, are relatively low, usually a few
hundred Ohms or less. Unlike classic analog and digital design, where virtually
infinite impedances are assumed, both voltage and current in the form of power
must be considered. To reduce errors and maximize sensitivity, maximum power
must be transferred from one circuit element to another.
From Ohm’s Law we learn that maximum power is transferred to a load if that load
resistance equals the source resistance. This applies even if the load and source
are reactive, that is, they have complex impedances.
2
Impedance Matching
• In this example, RL > RS
• Reactive elements (L,C) can be added
• Now ZS (RS + matching elements) = RL
Inductor “steps up” the impedance.
RS
Capacitor cancels or
“conjugates”
the residual reactance
RL
If the load does not match the source, impedance matching techniques can be
employed to improve the power transfer.
In this example, an inductor is added in series with the source resistance to increase
the impedance and then the resulting reactance is cancelled with a shunt capacitor.
The equivalent impedance across the capacitor now equals the load resistance and
maximum power is transferred. Power is lost in the matching elements proportional to
the “Q” or Quality of the elements and the amount of change in impedance. Q is a
measure of the resistance of an element. Current flow through a resistor results in a
reduction of voltage and a loss of power. This explains why the signal is not simply
transformed immediately to a nearly infinite impedance where it could be dealt with as
a voltage.
3
Smith Chart
Impedance matching can be done mathematically by transforming the impedances
back and forth from series to parallel. However, the complex math is awkward. A
graphical method of plotting impedance, known as the Smith Chart, was developed
in the days before computers. It enables the easy representation of complex
numbers and the development of matching networks. The Smith Chart is still useful
for displaying and working with complex impedances.
4
Constant Resistance Circles
0
1
25
50
100 200 500
The Smith Chart displays real and imaginary numbers on contours. The real part,
resistance, is plotted on circles which intersect at infinity. On this chart, we have
chosen 50 Ω as the systems impedance at the center of the chart.
5
Constant Reactance Lines
50 Ohms Inductive
100 Ohms Inductive
25 Ohms Inductive
200 Ohms Inductive
200 Ohms Capacitative
25 Ohms Capacitative
100 Ohms Capacitative
50 Ohms Capacitative
The imaginary, or reactive, part of the impedance is plotted on contours which,
again, converge on infinity. Positive reactance, series inductance, is plotted on the
top half of the chart. Negative reactance, series capacitance, is plotted on the lower
half of the chart.
6
Question
The Smith Chart is used to plot impedance. What is the
purpose of impedance matching in RF circuitry? Select the
correct answer and then click Done.
a. It ensures that the impedance matches the Load resistance (RL).
b. When a shunt capacitor is used in a circuit, its impedance must
match the Load and Source resistances.
c. It allows you to chart complex numbers and develop matching
networks.
d. It is used to improve power transfer when the RL and RS are not
equal.
Let’s take a moment to review what we achieve through impedance
matching.
Correct! Impedance matching is when you add one or more reactive
elements to a circuit in order to equal out the Load and Source impedances.
According to Ohm’s law, you won’t get maximum power transfer unless the
impedances are equal.
7
Linearity
• All components have a Dynamic Range
• Compression Point:
– Can be measured at the output or input
– For amplifiers, it’s usually the 1 dB gain reduction point
• Intercept point:
– Highly dependant on signal spacing
– Usually applied to the “third order” (f1 ± 2f2, or f2 ± 2f1) products
but sometimes “second order” (f2 ± f1, 2f1, 2f2)
– As a rule of thumb, for Amplifiers, IP3 is 10-15 dB higher than
1 dB Gain compression.
Linearity is a classic analog concept. Since modulated RF waves are analog signals, the
concept of linearity also becomes important in digital communications.
Every device has a linear range over which it faithfully reproduces or transfers any signal that
is presented to it. This range is known as a components Dynamic Range. Within that range,
the device does not affect the signal beyond its specified action.
However, every device also has a “compression point” which is the signal level at which the
device reaches a degree of non-linearity. In other words, it’s the point at which the device
begins to affect the signal. In an amplifier, the 1 dB gain compression point is often specified.
At this point, the amplifier’s gain is reduced by 1 dB and the amplifier is non-linear enough to
begin to impair the signals it should only be amplifying.
The concept of “intercept point” is more esoteric. This is the theoretical point at which the nonlinear products of two signals presented to an amplifier would equal the desired signals in
magnitude. In other words, suppose two signals that, when combined, surpassed the
compression point are passed through the device. The intercept point would be the theoretical
point at which the undesired products of the two signals were actually equal to the desired
output. These products, known as Intermodulation products, are the sum and difference of
the two signals and their multiples.
8
Input Third Order Intercept Point
In te rcep t
P o in t
+10
O u tp ut
3 rd O rde r
In te rcep t Po in t
L e ve l o f
Inp ut
S ign als
Output Level, dBm
0
-10
G a in
C o m p ress io n
-20
-30
S lop e = 1
-40
L e ve l o f
In te rm od u la tion
P ro du cts
-50
-60
-70
-80
-90
Inp ut
3 rd O rde r
In te rcep t P o in t
S lop e = 3
-10 0
-11 0
-50
-40
-30
-20
-10
0
+ 10
Inp ut L e ve l, d B m
IIP3
Non-linearity can be seen in the transfer characteristics of a device.
As the gain compresses, the transfer function, if described mathematically, includes
square and cube terms. If input signals are presented at these levels, the output signal
will contain these extra terms represented as spurious frequencies and distortion in the
desired signal’s phase and amplitude.
As the level the of input signals increases, the level of Intermodulation products
increases at a 3 to 1 rate. The theoretical intersection of the green gain line with the
red Intermodulation line is the intercept point. With complex modulation schemes, the
multiple tones composing a signal will be distorted and add to errors in recovery. Care
must be taken to choose components with enough dynamic range, to be able to
operate linearly.
9
Amplifier Classes of Operation
Class "A"
Collector current flows
for 360o of input signal
Class "AB"
Saturated
region
Collector current flows
for>180o but <360o of
input signal
Saturated
region
Collector current flows
for 180o of input signal
Class "C"
Saturated
region
Bias point
Collector current flows
for<180o of input signal
BVCER
Class "B"
BVCER
Bias point
BVCER
BVCER
Bias point
Saturated
region
Bias point
In order for an amplifier to maintain linearity, it must be able to supply the output power required by
its gain and the signal presented to it. This power is supplied by the amplifier’s bias circuit. The
bias circuit provides a quiescent current to the transistors and sets the amplifier’s class of
operation. The curves shown are collector current versus collector voltage (or drain current versus
drain voltage) device characteristics. These classes are actually carryovers from vacuum tube
amplifier terminology and really apply to only one amplifier stage.
Class A operation means that the device is biased on for the entire cycle of the input signal. This is
the most linear class but also the least efficient.
Class AB biases the amplifier on for most of the input signal’s cycle and represents a good linearity
compromise for most applications.
Class B operation has the device biased at turn-on so the device is on for only half the cycle. Class
B is often used with a differential pair of devices, with one transistor amplifying each half of the
input signal’s waveform.
Class C has no bias at all. The device is actually biased on by the input signal. There are other
classes where the device is actually reverse biased. Class C and other non-linear classes have
high efficiency due to the high harmonic content of the output signal. Harmonics are multiples of
the signal’s fundamental frequency and are only acceptable in FM systems. For an amplifier to
have better than approximately 25% efficiency, the output must contain harmonics.
10
Question
Complete the following sentence, and then click Done.
The power required in order for an amplifier to maintain linearity is supplied
by its _____________.
a)
b)
c)
d)
bias circuit
amplifier
input signal
gain compression
Do you remember which component of an amplifier allows it to maintain
linearity?
Correct! The power required in order for an amplifier to maintain linearity is
supplied by its bias circuit.
11
Noise
•
Noise limits system sensitivity
•
All component in a system add to the system noise
•
The minimum Noise Power in a system can be described by:
Noise Power (Watts) = kTB
where k = Boltzmann’s Constant, 1.38 x 10-23J/°K
T = Temperature in °K
B = Bandwidth in Hz
At 26°C, Noise Power = -174 dBm + 10logBW (Hz)
•
Solutions:
– limit the bandwidth of the system
– limit the noise produced by system components
Noise limits the sensitivity of communications systems. RF signals are analog and,
therefore, compete with noise power in a communications system. The ratio of
desired signal-to-noise is an important consideration. Demodulation schemes rely
on a minimum signal-to-noise ratio to recover information.
All components in a system contribute to noise. Noise, if great enough, will mask
the desired signal making it impossible to recover and demodulate. Every system
has what is often referred to as a “noise floor.” This minimum noise power is the
thermal noise that is generated at a given temperature.
The noise floor in any system is a function of its bandwidth, temperature, and
Boltzmann’s constant as shown.
We can limit the noise power by limiting the bandwidth we use in the system.
Unfortunately, high data-rate systems require a higher bandwidth. Therefore, in
these systems we must deal with higher thermal noise than in low data-rate
systems. We can also limit the non-thermal noise generated by the components in
the system.
12
Noise Factor/Noise Figure
The contribution to system noise by a component:
• Noise Factor (numeric) = S/N at input
S/N at output
• Noise Figure (dB) = S/N (dB) at input - S/N at output
= 10log Noise Factor
Devices themselves contribute to the noise power in a system beyond their thermal
noise. As a signal passes through a device, the device adds its own noise to the
signal.
A measure of added noise is Noise Factor,…
…or in dB, Noise Figure.
Devices with loss have noise figures equal to their loss in dB. Devices with gain can
actually improve the signal-to-noise ratio if they amplify the signal more than the
level of noise added. Devices designed specifically for this purpose are known as
low-noise amplifiers or LNAs.
13
Cascaded Noise Figure
•The Cascaded noise figure of a system is described by:
Cascaded NF (numeric) = NFprevious stage + NFcurrent stage-1
Gain previous stages
•Note the influence of the Gain and NF of the previous stage
•System noise figure is set primarily by the first few stages
As the signal and noise move through a system, the noise performance of the
system “cascades” and can be calculated as shown. Note that a high-gain, lownoise device can effectively set the noise figure of a system. This is the main
function of low noise amplifiers in communications systems. The system noise
figure is a direct indication of the sensitivity of the system and, therefore, its
effective range for a given bit error performance.
14
Question
Select the options below that represent methods for reducing
noise in a system. Select all that apply and then click
Done.
a) Make sure the input voltages do not exceed the output voltage.
b) Limit the bandwidth of the system.
c) Use a low-noise amplifier to amplify the signal more than the
noise added.
d) Use only high-gain/low-noise devices in your system so that you
can set a low noise figure.
Let’s review what you’ve learned about reducing noise in a system.
Correct! To reduce noise, you can limit the bandwidth of your system since
the noise floor is a function of bandwidth and temperature. However, this is
not really an option for high data-rate systems that require a high bandwidth.
A better way to reduce noise is to use a low-noise amplifier. An LNA will
improve the signal-to-noise ratio by amplifying the signal more than the level
of noise added by the devices in the system.
15
Module Summary
This module has covered the following elements
of wireless communications:
–
–
–
–
Impedance matching
Power transfer
Linearity
Noise
In this module, you learned about various considerations to take into account when
creating wireless communication systems, such as impedance matching, power
transfer, linearity, and noise.
16