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SVKM’S NMIMS
Mukesh Patel School of Technology Management & Engineering
Department of Electronics &Telecommunication Engineering
Advanced Communication Lab
Subject: Radio Frequency Circuit Design
Experiment No. 1
Aim:
RF behavior of Passive components and high frequency resistor.
Objective:
To learn introduction to behavior of Passive components and high frequency resistor
Introduction to Radio Frequency:
Radio frequency (RF) engineering is a subset of electrical engineering that deals with devices
that are designed to operate in the Radio Frequency spectrum.
These devices operate within the range of about 3 KHz up to 300 GHz
An RF module is a small electronic circuit used to transmit and/or receive radio signals on
one of a number of carrier frequencies. RF modules are widely used in electronic design
owing to the difficulty of designing radio circuitry
RF engineering is incorporated into almost everything that transmits or receives a radio wave,
which includes, but is not limited to, Mobile Phones, Radios, Wi-Fi, and two-way radios.
RF engineering is a highly specialized field falling typically in one of two areas;
1. Providing or controlling coverage with some kind of antenna/transmission system
and
2. Generating or receiving signals to or from that transmission system to other
communications electronics or controls.
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To produce quality results, an in-depth knowledge of mathematics, physics,
general electronics theory as well as specialized training in areas such as wave
propagation, impedance transformations, filters, micro strip circuit board design, etc.
may be required.
Importance of radio frequency design:
Wireless communications (explosive growth of cell phones)

Global positioning systems (GPS)

Computer engineering (bus systems, CPU, peripherals exceeding 600 MHz)
Wire:
Wire in an RF circuit can take many forms.
Wire wound resisters, inductors, and axial-and radial-leaded capacitors all use a wire of some
size and length either in their leads, or in the actual body of the components, or both.
Wire is also used in many interconnect applications in the lower RF spectrum.
The behavior of a wire in the RF spectrum depends to a large extent on the wire’s diameter
and length.
To standardize the size of wire, the American Wire Gauge (AWG) System Commonly used
in the United States.
In American Wire Gauge (AWG) System the size of wire is measured in mil.
1 mil = 2.54X 10-5 m = 0.001 inch
In the AWG (American Wire Gauge) Systems, the diameter of a wire roughly doubles every
six wire gauges.
Example 1:
Given that the diameter of AWG 50 wire in 1.0 mil (0.001inch),
What is the diameter of AWG 14 wire?
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Skin Effect:
A conductor, at low frequencies, utilizes its entire cross-sectional area as a transport medium
for charge carriers.
As the frequency is increased, an increased magnetic field at the center of the conductor
presents impedance to the charge carriers, thus decreasing the current density at the center
of the conductor and increasing the current density around its perimeter.
This increased current density near the edge of the conductor is known as “Skin Effect”.
It occurs in all conductors including resistor leads, capacitor leads, and inductor leads.
The depth into the conductor at which the charge-carrier current density falls to 37% of its
value along the surface, is known as the skin depth and is a function the frequency and the
permeability and conductivity of the medium.
Thus, different conductors, such as Silver, Aluminum, and Copper, all have different skin
depths.
The attenuation constant for the conducting medium is give as
α = √π f μ σ
Therefore the skin depth for the conducting medium is given as
δ =
1
1
=
α
√π f μ σ
The net result of skin effect is an effective decrease in the cross-sectional area of the
conductor and, therefore, a net increase in the AC resistance of the wire.
For copper, the skin depth is approximately 0.85 cm at 60 Hz and 0.007 cm at 1 MHz Or, to
state it another way : 63% of the RF current flowing in a copper wire will flow within a distance
of 0.007 cm of outer edge of the wire.
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A1 = Area of Inner Conductor = π r12
A2 = Area of Outer Conductor = π r22
Area of skin depth = A2 − A1
= π (r2 − r1 )
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Straight-Wire inductors
In the medium surrounding any current-carrying conductor, these exists a magnetic field.
If the current in the conductor is an alternative expanding and contracting and, thus,
producing a voltage on the wire which oppose any charge in current flow.
This opposition to change is called self-inductance and we call anything that possesses this
quality as an inductor.
The inductance of a straight wire depends on both its length and diameter
Where
Example 2:
Find the inductance of 5 cm of NO. 24 copper wire with its diameter of 25.3 mils.
The concept of inductance is important because any and all conductors at radio frequencies
(including hookup wire, capacitor leads, etc.) tend to exhibit the property of inductance.
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High Frequency Resistors
Resistance is the property of a material that determines the rate at which electrical energy is
connected into heat energy for a given electric current.
The equivalent circuit of a resistor at radio frequencies is given as
Where



“R” is the resistor value.
“L” is the lead inductance.
“C” is a combination of parasitic capacitance which varies from resistor
to resistor depending on the resistor’s structure.
Carbon-composition resistors
Carbon-composition resistors are notoriously poor high-frequency performance. A carboncomposition resistor consists of densely packed dielectric particulates or carbon granules.
Between each pair of carbon granules is a very small parasitic capacitor. These parasites, in
aggregate, are not insignificant, however, and are the major component of the device’s
equivalent circuit.
Wire wound resistors
Wire wound resistors have problems at radio frequencies too. As may be expected, these
resistors tend to exhibit widely varying impedances over various frequencies.
This is particularly true of the low resistance values in the frequency range of 10 MHz to 200
MHz. The inductor L, shown in the equivalent circuit is much larger for a wire wound resistor
then for a carbon-composition resistor.
Wire wound resistors look like inductors their impedances will first increase as the frequency
increases. At some frequency (Fr), however, the inductance (L) will resonate with the shunt
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capacitance (C), producing an impedance peak. Any further increase in frequency will cause
the resistor’s impedance to decrease as shown
A metal-film resistor
A metal-film resistor seems to exhibit the best characteristics over frequency. Its equivalent
circuit is the same as the carbon-composition and wire wound resistor, but the values of the
individual parasitic elements in the equivalent circuit decrease.
The impedance of a metal-film resistor tends to decrease with frequency above about 10
MHz. This is due to the shunt capacitance in the equivalent circuit.
At very high frequencies, and which low-value resistors (under 50Ω), lead inductance and
skin effect may become noticeable.
The lead inductance produces a resonance peak, as shown for the 5Ω resistance and skin
effect decrease the slop of the curve as if falls off with frequency.
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Example3:
In Fig (Resistor equivalent circuit). The lead lengths on the resistor are 1.27 cm (0.5 inch),
and are made up of AWG14 wire. The total stray shunt capacitance is 0.3 pF. If the resistor
value is 10,000 ohms, what is its equivalent RF impedance at 200 MHz?
RF behavior of Carbon Composition Resistors:
Matlab Code:
clc;
close all;
c=2e-12;
r=2000;
l=7;
mil=2.54e-3;
d=64*mil;
L=0.002e-6*l*([2.3*log(4*l/d)]-.75);
f=1e6:10e6:500e6;
XL=2*pi*f*L*i
XC=-i./(2*pi*f*c);
Z=(r+2*XL).*(XC)./(r+2*XL+XC);
plot(f,abs(Z));
xlabel('frequency in MHz');
ylabel('Zeq in ohm');
title('RF Behaviour of Carbon Composition Resistor')
Output:
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RF Impedance Behavior of Metal Film Resistors:
1. Plot the Impedance behavior of metal film of 500 Ω resistor with 2.5 cm copper
connections of AWG 26 and a stray capacitance of 5 pF as shown below.
Plot the response using MATLAB Code. Given
σCU = 64.516 X 10 6 Ω−1 ⁄m
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RF behavior of Metal-film Resistors:
Matlab Code:
Output:
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Conclusion:
Hence we have studied the RF behavior of carbon composition and metal film resistors and
observed the output for the same.
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