PVP22

Code: 22ECMC2T6B

I M.Tech - II Semester- Regular/Supplementary Examinations AUGUST 2024

RF IC DESIGN
(MICROWAVE & COMMUNICATION ENGINEERING)

1. (a) Describe briefly how passive components are realized in RF IC Design

RESISTORS:

There are relatively few good resistor options in standard CMOS (complementary metal-
oxide silicon) processes. One possibility is to use polysilicon (“poly”) inter¬ connect
material, since it is more resistive than metal.Resistivities tend to be in the vicinity of roughly
5-10 ohms per square (within a factor of about 2-4, usually), so poly is appropriate mainly for
moderately small-valued resistors.

Resistors made from source-drain diffusions are also an option. The resistivities are generally
similar (within a factor of 2, typically) to those of silicided polysilicon.

In modern VLSI (very large-scale integration) technologies, source-drain “diffusions” are

defined by ion implantation. The source-drain regions formed in this way are quite shallow
(usually no deeper than about 200-300 nm, scaling roughly with channel length), quite
heavily doped, and almost universally silicided, leading to moderately low temperature
coefficients (order of 500-1000 ppm/°C).
Wells may be used for high-value resistors, since resistivities are typically in the range of 1-
10 kQ per square.

A MOS transistor is used as a resistor, even a variable one. With a suitable gate-to-source
voltage, a compact resistor can be formed. From first-order theory, recall that the incremental
resistance of a long-channel MOS transistor in the triode region.

1
Capacitors

All of the interconnect layers may be used to make traditional parallel plate capacitors (see
Figure). However, ordinary interlevel dielectric tends to be rather thick (order of 0.5-1 gm),
precisely to reduce the capacitance between layers.

Figure: parallel plate capacitor

The standard capacitance formula,

C=εA/H= εWL/H

A standard alternative is to use a MOS capacitor, available in CMOS processes as simply the
gate capacitance of an ordinary transistor.Capacitance per unit area depends on the dielectric
thickness, but is typically in the range of 1-5 fF//um 2, or roughly 20-100 times larger than
ordinary interconnect capacitors.

Another option is to use a junction capacitance, such as that formed by a p+ region

in an n-well. Since a junction capacitance depends on the applied bias, such a ca¬
pacitor is often exploited to make electronically tuned circuits; diodes used this way
are known as varactors (from variable reactor).

INDUCTORS

SPIRAL INDUCTORS
The only widely used on-chip inductor is the planar spiral, a square version of which is
shown in Figure

2
Figure spiral Inductor

Another case of interest is the inductance of a single loop of wire. Despite the simplicity of
the structure, there is no exact, closed-form expression for its inductance (elliptic functions
arise in the computation of the total flux). However, a useful approximation is given by
L =µπr
This formula tells us that a loop of 1 mm radius has an inductance of approximately 4nH.

3
1(b)Compare the characteristics of co-axial line, two -wire line and a parallel plate
transmission line.

The transmission line is defined as the path of carrying alternating electrical energy from
source to load.

Comparison Summary:

Parallel Plate
Characteristic Coaxial Line Two-Wire Line
Transmission Line
Impedance Typically 50 or 75 ohms 100 - 600 ohms Design dependent
Shielding Excellent Poor None
Power
Moderate to high Moderate to high High
Handling
Frequency
DC to hundreds of GHz Low to several MHz Low to a few GHz
Range
Low (depends on Low to moderate (depends
Losses Moderate
construction) on modes)

RF, cable TV, internet, Telephony, antenna

Applications Microwave circuits, filters
instrumentation feed lines
Good EMI shielding, low Simple, low cost, low
Advantages High power handling,
radiation loss loss
Lack of shielding, higher-
order mode issues
Bulkier, more expensive High radiation loss,
Disadvantages
at high freq. susceptible to EMI

4
2(a) Explain Passive impedance transformation

Passive impedance transformation is a technique used in RF (Radio Frequency) Integrated

Circuit (IC) design to match the impedance of different circuit components or stages. The
goal is to maximize power transfer, minimize reflections, and optimize the performance of
RF circuits. This is particularly important in high-frequency applications where mismatched
impedances can lead to significant power loss and degraded signal integrity.

Key Concepts in Impedance Transformation:

1. Impedance Matching:
o Impedance matching involves adjusting the impedance of one circuit (or
device) to match the impedance of another circuit (or device). When the
impedances are matched, maximum power transfer occurs, and signal
reflections are minimized.
o In RF design, a common goal is to match the impedance of the source (e.g., an
antenna or RF signal generator) to the impedance of the load (e.g., an
amplifier input or transmission line) to ensure efficient power transfer.
2. Passive Components:
o Resistors, inductors, and capacitors are the primary passive components
used in impedance transformation networks. These components do not require
any external power to operate; they rely on the inherent properties of their
materials to perform impedance transformation.
3. Network Types:
o There are several types of impedance matching networks commonly used in
RF design, including L-networks, T-networks, Pi-networks, and
transformers. Each network has its own advantages and use cases, depending
on the desired transformation ratio, frequency range, and circuit topology.

Common Passive Impedance Transformation Networks:

1. L-Network:
o The simplest form of impedance transformation network, consisting of two
reactive components (an inductor and a capacitor) arranged in an "L" shape.
o There are two configurations for the L-network:
 Low-Pass L-Network: One component is in series with the signal path
(usually an inductor), and the other is in shunt to ground (usually a
capacitor).
 High-Pass L-Network: The series component is a capacitor, and the
shunt component is an inductor.
o Operation:

5
  By selecting appropriate values for the inductor and capacitor, the
impedance seen at one side of the network can be transformed to match
the impedance of the other side.
o Advantages: Simple, minimal component count, effective for narrowband
applications.
o Disadvantages: Limited flexibility, mainly used for transforming between
specific impedance ratios.
2. Pi-Network:
o Consists of two capacitors (or inductors) and one inductor (or capacitor)
arranged in a shape that resembles the Greek letter "π".
o Commonly used in RF amplifiers and tuners.
o Operation:
 Offers more flexibility than an L-network, allowing for greater control
over bandwidth and impedance transformation.
 Can provide both low-pass or high-pass filtering characteristics.
o Advantages: Greater flexibility in design, can achieve higher Q (quality
factor), and better bandwidth control.
o Disadvantages: More components and complexity compared to an L-network.
3. T-Network:
o Consists of two inductors (or capacitors) and one capacitor (or inductor)
arranged in a "T" shape.
o Used in impedance matching over a wider range of impedances and
frequencies.
o Operation:
 Allows impedance transformation and provides additional control over
bandwidth and filter characteristics.
o Advantages: Suitable for broadband applications, more flexible in terms of
impedance transformation.
o Disadvantages: More complex than L-networks, higher component count.
4. Transformers:
o RF transformers are passive components that can transform impedances by
utilizing the turns ratio between the primary and secondary windings.

Applications of Impedance Transformation in RF IC Design:

1. Maximizing Power Transfer:

o Impedance transformation networks are used to ensure maximum power
transfer between different stages of an RF circuit, such as between a source
and an amplifier, or between an amplifier and an antenna.
2. Minimizing Reflections:
o By matching impedances, reflections that occur due to impedance
discontinuities are minimized, which is particularly crucial in high-frequency
applications where signal reflections can lead to interference and signal
degradation.
3. Impedance Matching in Antenna Design:
o Antennas are often designed to have a characteristic impedance (e.g., 50
ohms) that must be matched to the impedance of the transmission line and
receiver circuit to ensure efficient signal reception.
6
 4. Filter Design:
o Impedance transformation networks can also serve dual purposes in filter
design, providing impedance matching while also shaping the frequency
response of the circuit.
5. Noise Matching in Low Noise Amplifiers (LNAs):
o In RF front-end design, especially in receivers, impedance transformation
networks are used to optimize the noise figure of the amplifier by matching
the source impedance to the impedance that minimizes the noise figure of the
LNA

Passive impedance transformation is a fundamental technique in RF IC design, crucial for

optimizing performance, minimizing losses, and ensuring efficient power transfer across
different stages of an RF system. By understanding the characteristics and applications of
various impedance transformation networks, designers can effectively implement impedance
matching strategies tailored to their specific circuit requirements.

2(b) Define available power gain and describe

Friis equation for noise figure

available power gainis the ratio of available DUT power to

available source power. Note that the available power was
defined as the maximum power capable of being delivered by
a source to a load under conditions of conjugate matching and
that AVAILABLE GAIN is only defined under conditions of
CONJUGATE MATCHING

Friis Equation for Noise Figure in RF IC Design

The Friis equation (or Friis formula) is a fundamental equation in RF (Radio Frequency)
and microwave engineering used to calculate the overall noise figure of a cascaded system,
such as a chain of amplifiers or other RF components. Understanding and applying the Friis
equation is essential for RF IC designers to ensure minimal degradation of the signal-to-noise
ratio (SNR) as the signal passes through multiple stages.

Definition of Noise Figure (NF):

 Noise Figure (NF) is a measure of how much noise an RF component (like an

amplifier) adds to the signal it processes. It is a key parameter in RF systems because
it directly affects the overall sensitivity and performance of the receiver.
 Mathematically, the noise figure FFF is defined as the ratio of the signal-to-noise
ratio (SNR) at the input to the SNR at the output:

7
  The noise figure is usually expressed in decibels (dB):

Friis Equation for Noise Figure of Cascaded Stages:

When an RF signal passes through multiple stages in a receiver or amplifier chain, each stage
contributes to the overall noise figure of the system. The Friis equation provides a way to
calculate the total noise figure of the system based on the noise figures and gains of the
individual stages.

Noise factor (F) is the ratio of signal-to noise ratio (SNRi) at input to the signal-to-noise ratio
(SNRo) ratio at the output of a circuit/device.

The Noise figure (NF) is defined as decibel of Noise factor. i.e.,

n-
stage cascaded amplifier
If “n” number of devices are connected in the cascaded manner (for example, a multistage
amplifier with n stage), then the total noise factor can be calculated by Friis formula as given
below. Here, the noise factor (F) is the ratio of signal-to noise ratio (SNRi) at input stage to
the signal-to-noise ratio (SNRo) ratio at the output stage of the multistage-amplifier.

8
Therefore, total noise figure,

From the formula, we can understand that the first amplifier of a multistage amplifier has a
significant effect on the total noise figure; because the noise factor of the following stages is
reduced by the stage gains. So, the first stage of the cascaded amplifier usually has a low
noise figure and the noise figure requirements of other following stages usually more relaxed.

 Where:
 F- Total noise factor
 F1- Noise factor of the first stage
 F2-Noise factor of second stage
 F3- Noise factor of third stage
 Fn- Noise factor of nth stage
 NFT – Total noise factor
 G1 – Power gain of the first stage
 G2- Power gain of the second stage
 Gn- Power gain of the nth stage

9
UNIT II

3(a) Differentiate neutralization andunilateralization in High frequency amplifierdesign

One strategy derives naturally from recognizing that the problem stems from coupling the
input and output ports. Removing the coupling should therefore be of benefitOne strategy
derives naturally from recognizing that the problem stems from coup¬
ling the input and output ports. Removing the coupling should therefore be of benefit

unilateralization

Figure :Cascode amplifier with single tuned load.

This decoupling of output from input should feel familiar- it is precisely what eliminates the
Miller effect from common-source amplifiers.By providing isolation between input and
output portswith the common-gate stage, we eliminate (or at least greatly suppress) detuning
andthe potential for instability, thus allowing the attainment of larger gain-bandwidth
products.
“unilateral” amplifiers, that is, ones in which signals can How only one way over large
bandwidths

10
neutralization

Figure: Neutralized common-source amplifier

If we cannot (or choose not to) eliminate undesired feedback, another approachis to cancel it
to the maximum possible extent. Since this cancellation is rarely perfect over large
bandwidths, this approach is generally called “neutralization” to distinguish it from more
broadband unilateralization techniques that do not depend oncancellations.The classic
neutralized amplifier is shown in Figure. Notice that the inductorhas been replaced by
something slightly more complex: a tapped inductor, or autotransformer. By symmetry, the
voltages at the top and bottom of the inductor are exactly 180° out of phase in the connection
shown. Therefore, the drain voltage and the voltage at the top of neutralizing capacitor Cn are
180° out of phase. Now, if theundesired coupling from drain to gate is due only to Cga then,
by symmetry, selectionof Cn equal to guarantees that there is no net feedback from drain to
gate! Thecurrent through the neutralizing capacitor is equal in magnitude and opposite in
signto that through Cgd\ we have removed the coupling from output to input by adding
more coupling from output to input (it’s just out of phase so that the net coupling is
zero).

3(b) Explain bandwidth enhancement with a shuntseries amplifier

an alternative approach to the design of broadband amplifiers is to use negative feedback.

One particularly useful broadband circuit that employs negative feedback is the shunt-series
amplifier. Its name derives from the use of a combination of shunt and series feedback.

Figure:Shunt-series amplifier (biasing not shown)

stripped of biasing details, the shunt-series amplifier is depicted in Figure.the voltage gain of
the amplifier from the gate to the drain is approximately RL/R1.

11
Although we have assumed that Rf has but a minor effect on gain, it has a controlling
influence on the input and output resistance.
Specifically, it reduces bothquantities through the (shunt) feedback it provides. Additionally,
the reduction ofinput and output resistances helps to increase the bandwidth still further.

Just as in the classic Miller effect, connecting an impedanceacross two nodes that have an
inverting gain between them results in a reduction ofimpedance. The ease with which this
amplifier provides a simultaneous impedance match atboth input and output ports accounts in
part for its popularity.

4(a) Discuss the behaviour of LNA topologies withits design constraints

Low Noise Amplifier (LNA) Topologies and Their Design Constraints in RF IC Design

Low Noise Amplifiers (LNAs) are crucial components in RF IC (Radio Frequency

Integrated Circuit) design, especially in receiver front-ends. LNAs are designed to amplify
weak signals received from an antenna while adding minimal noise. The performance of an
LNA is characterized by its noise figure (NF), gain, linearity, input/output impedance
matching, and power consumption. Different LNA topologies have unique behaviors and
design constraints that must be carefully considered during the design process.

Common LNA Topologies:

1. Common-Source (CS) / Common-Emitter (CE) LNA

2. Common-Gate (CG) / Common-Base (CB) LNA
3. Cascode LNA
4. Inductive Degeneration LNA
5. Differential LNA

Let's discuss each of these topologies, their behaviors, and design constraints.

12
1. Common-Source (CS) / Common-Emitter (CE) LNA

 Behavior:
o The common-source (CS) configuration for MOSFETs (or common-emitter
(CE) for BJTs) is a widely used topology due to its high gain and relatively
simple structure.
o The transistor's gate (or base) serves as the input, the drain (or collector) as the
output, and the source (or emitter) is grounded or connected to a low
impedance path.
o The input signal is applied to the gate (or base), and the output is taken from
the drain (or collector).
 Design Constraints:
o Noise Figure (NF): The noise figure is affected by the thermal noise of the
input transistor and the matching network. To minimize noise, the input
matching network should be designed to present an optimum source
impedance that minimizes the overall NF.
o Impedance Matching: Achieving simultaneous noise and power matching is
challenging. The input impedance needs to be matched to the source
impedance (often 50 ohms) while maintaining a low NF.
o Gain: The gain is determined by the transconductance (gmg_mgm) of the
transistor and the load impedance. High gain requires high gmg_mgm and a
carefully chosen load.
o Linearity: Non-linearity in the CS/CE topology can lead to intermodulation
distortion. Biasing conditions and the choice of operating point are critical for
maintaining linearity.
o Stability: The CS/CE topology can suffer from instability due to parasitic
capacitances, especially at high frequencies. Stability is ensured by proper
layout techniques and the use of feedback or neutralization.

2. Common-Gate (CG) / Common-Base (CB) LNA

 Behavior:
o The common-gate (CG) configuration for MOSFETs (or common-base (CB)
for BJTs) is used for wideband applications due to its inherently wide
bandwidth.
o In this topology, the source (or emitter) is the input, the drain (or collector) is
the output, and the gate (or base) is grounded or AC-coupled to ground.
o This configuration offers a low input impedance, making it suitable for
wideband impedance matching.
 Design Constraints:
o Noise Figure (NF): The NF of CG/CB LNAs is typically higher than that of
CS/CE configurations due to the noise contribution from the input transistor.
However, at high frequencies, this topology can provide a lower NF because it
reduces the effect of gate/drain overlap capacitance.
o Impedance Matching: The low input impedance (approximately
1/gm1/g_m1/gm) makes it easier to match to a low source impedance, which
is beneficial for wideband applications.
o Gain: Gain is typically lower than that of the CS/CE topology. However, gain
can be enhanced with appropriate inductive loading.

13
 o Linearity: The CG/CB topology generally provides good linearity due to its
low input impedance and better control over the bias point.

3. Cascode LNA

 Behavior:
o The cascode configuration combines a common-source (CS) or common-
emitter (CE) stage with a common-gate (CG) or common-base (CB) stage.
o This topology enhances gain and provides better isolation between input and
output, reducing the Miller effect and improving bandwidth.
 Design Constraints:
o Noise Figure (NF): The cascode topology offers a lower NF than the CG/CB
configuration while providing good gain. The NF mainly depends on the first
(common-source/common-emitter) stage.
o Impedance Matching:Cascode LNAs can achieve good input impedance
matching with proper design of the input matching network, often using
inductive degeneration.
o Gain: The cascode provides high gain due to its increased output resistance
and reduced Miller capacitance. Gain depends on the transconductance of the
input transistor and the impedance at the output.
o Linearity:Cascode LNAs offer good linearity because the second transistor
(common-gate or common-base) reduces the voltage swing at the drain of the
first transistor, mitigating distortion.

4. Inductive Degeneration LNA

 Behavior:
o Inductive degeneration involves adding an inductor in series with the source
(or emitter) of the input transistor.
o This technique is used to provide a real part to the input impedance, making
impedance matching easier.
 Design Constraints:
o Noise Figure (NF): Inductive degeneration improves NF by optimizing
impedance matching. It reduces the noise contribution from the input
matching network.
o Impedance Matching: The input impedance can be set to match the source
impedance (e.g., 50 ohms) by selecting an appropriate inductor value,
allowing simultaneous noise and power matching.
o Gain: The gain is slightly reduced due to the degenerative effect of the
inductor, which lowers the overall transconductance. However, this can be
compensated by proper design of the load network.
o Linearity: The addition of the inductor improves linearity by providing
negative feedback, reducing distortion.

5. Differential LNA

 Behavior:
o A differential LNA consists of two transistors in a differential pair
configuration. This topology is used to reject common-mode noise and
improve the signal-to-noise ratio (SNR).

14
 o Differential LNAs provide good balance and are less sensitive to substrate
noise and supply variations.
 Design Constraints:
o Noise Figure (NF): The differential structure typically offers a slightly higher
NF than single-ended designs due to the addition of another noise source.
However, differential signaling improves SNR by rejecting common-mode
noise.
o Impedance Matching: Differential LNAs require careful matching of both
input sides to maintain balance. The input network must be symmetric to
ensure proper differential operation.
o Gain: Differential LNAs provide high gain, similar to single-ended
topologies, but the gain must be balanced between the two paths.
o Linearity: Differential operation inherently improves linearity by canceling
even-order distortion products, providing better performance for large signals.

4(b) Design a low noise amplifier using MOSFETwith Noise Figure <=4dB

Any design example like this

Figure: Schematic of Designed cascode LNA at 3.5GHz

The procedure starts with four knowns: the frequency ofoperation, ω0, the value of the
degeneration inductance, Ls, and the value of the input seriesinductance, Lg. Each of the last
three variables is slightly flexible, but it is good to select somevalues to complete the design,
and make iterations if necessary.The design starts with the following two equations:

15
With ω0 =3.5GHz known, Cgs and ωT and gm (= ωTCgs) is calculated from above equations

The design procedure now continues with selecting a value for Ldsuch that it resonates
at ω0.Choose cd= CL= 5pf to 10pf calculate Ld

The foregoing procedure typically leads to a design with a relatively low noise figure,
<=4dB(approximately 2.2 dB)

5(a) List the advantages of subsampling mixers

Subsampling, also known as downsampling, is a signal processing technique used to reduce

the sampling rate of a digital signal. It involves taking a subset of the original samples from
the signal, effectively reducing the number of samples while preserving the essential
characteristics of the signal.

The process of subsampling typically follows these steps:

16
 1. Lowpass filtering: Before subsampling, the signal is passed through a lowpass filter
to remove high-frequency components that could lead to aliasing during the
subsequent downsampling step.
2. Downsampling: The lowpass-filtered signal is then subsampled by keeping only
every Nth sample, where N is the subsampling factor. This reduces the sampling
rate of the signal by a factor of N.
The primary reasons for subsampling include:

1. Reducing data size: By decreasing the sampling rate, the amount of data required to
represent the signal is reduced, which can be beneficial for storage, transmission, or
processing.
2. Computational efficiency: Subsampling can decrease the computational burden in
subsequent signal processing operations, as the number of samples to be processed
is reduced.
3. Anti-aliasing: The lowpass filtering step helps to prevent aliasing, which can occur
when the signal is sampled at a rate that is too low relative to its highest frequency
component.
Subsampling is widely used in various applications, such as image and video processing,
where high-resolution data can be downscaled to a lower resolution for efficient storage,
transmission, or display. It is also commonly employed in digital signal processing, where the
sampling rate of a signal may be reduced to match the requirements of a particular algorithm
or hardware implementation.

Subsampling mixers provide several advantages in modern RF and digital communication

systems, especially when considering power efficiency, cost, flexibility, and compatibility
with digital processing. These benefits make subsampling mixers an attractive choice in
applications such as software-defined radios (SDRs), low-power communication devices, and
wideband receivers. However, it is important to carefully manage potential drawbacks such
as aliasing and noise folding to fully leverage the advantages of subsampling mixers.

5(b) Explain the operation of passive and active mixers.

The essential characteristic of a mixer is that it produces a component in its output which is
the product of the two input signals. Both active and passive circuits can realize mixers.
Passive mixers use one or more diodes and rely on their non-linear relation between voltage
and current to provide the multiplying element. In a passive mixer, the desired output signal
is always of lower power than the input signals.

Working Principle of Passive Mixers

To understand the operation of passive mixers in more detail, let's look at how a typical diode
ring mixer works:

17
 1. Input Signals: The RF input signal (at frequency fRFf_{RF}fRF) is fed into the
mixer along with a strong LO signal (at frequency fLOf_{LO}fLO). The LO signal is
typically much stronger than the RF signal to ensure the proper switching of the
diodes or transistors.
2. Switching Action: The LO signal drives the diodes or transistors to switch between
conducting and non-conducting states. In the case of a diode ring mixer, when the LO
signal is positive, one set of diodes conducts, and when the LO signal is negative,
another set conducts.
3. Mixing Process: The switching action caused by the LO signal effectively modulates
the RF signal. This modulation results in the creation of new frequency components at
the output. These components are at fRF+fLOf_{RF} + f_{LO}fRF+fLO and
fRF−fLOf_{RF} - f_{LO}fRF−fLO, along with harmonics of both signals. The
desired frequency component (often fIF=∣fRF−fLO∣f_{IF} = |f_{RF} - f_{LO}|fIF
=∣fRF−fLO∣) is selected using an output bandpass filter.
4. Output Signal: The output signal is then filtered to remove unwanted frequency
components, leaving only the desired intermediate frequency (IF) signal.

Active Mixers in RF Integrated Circuits (RFICs)

Active mixers are crucial components in RF (Radio Frequency) integrated circuits (ICs) used
for frequency conversion in wireless communication systems. Unlike passive mixers, which
rely solely on passive components such as diodes or switches, active mixers utilize active
devices like transistors (bipolar junction transistors (BJTs), field-effect transistors (FETs), or
MOSFETs) to provide gain and improve performance metrics such as noise figure and
linearity. This makes active mixers ideal for applications requiring higher performance, such
as mobile communications, satellite communications, and high-frequency data links.

Mixers are used in a variety of RF/microwave applications, including military radar, cellular
base stations, and more. An RF mixer is a three-port passive or active device that can
modulate or demodulate a signal. The purpose is to change the frequency of an
electromagnetic signal while (hopefully) preserving every other characteristic (such as phase
and amplitude) of the initial signal. A principal reason for frequency conversion is to allow
amplification of the received signal at a frequency other than that of the RF.

Figure: A mixer presented symbolically.

Figure 1 shows the mixer’s three ports: fin1 and fin2 are the input ports while the output port
is the both the sum and the difference in frequency of the inputs:

fout = fin1 ± fin2

18
 Figure: Representation of downconversion and upconversion.

The three ports (Figure) are referred to as the RF input port, LO (local oscillator) input port,
and the IF (intermediate frequency) output port. A mixer is also known as a downconverter if
the mixer is part of a receiver or as an upconverter if it is part of a transmitter.

Depending upon the application in which the mixer is being used, the LO is typically driven
with either a sinusoidal continuous wave signal or a square wave. In concept, the LO signal
acts as a gate of the mixer in which the mixer is considered ON when the LO is a large
voltage and OFF when it is a small voltage. The LO can only be an input port, while the RF
and IF ports can be interchanged between the second input or output.

19
6(a) Explain multiplier-based mixer.

The Gilbert Cell Mixer

Multiplier-Based Mixer Circuit Design

A common implementation of a multiplier-based mixer is the Gilbert cell mixer, which is

widely used in RFICs due to its good performance and ease of integration in CMOS and
bipolar technologies.

Gilbert Cell Mixer Design:

The Gilbert cell mixer is essentially a differential amplifier followed by a differential pair of
transistors configured in a cross-coupled fashion. Here’s how it works:

1. Differential Amplifier Stage:

o The RF signal is fed into a differential amplifier formed by a pair of transistors
(e.g., MOSFETs or BJTs). This stage amplifies the RF signal and converts it
into a differential form.

2. Switching Quad:
o The LO signal is applied to a switching quad of transistors. The LO signal
alternately switches the transistors on and off in a balanced manner,
effectively multiplying the RF signal by a square-wave version of the LO
signal.
o This switching action effectively performs a multiplication of the RF signal by
the LO signal, achieving the desired mixing action.

3. Output Signal:
o The output from the switching quad contains both the sum and difference
frequency components of the RF and LO signals. A subsequent filtering stage

20
 (low-pass or band-pass) selects the desired IF output signal and rejects the
unwanted components.

6(b) Discuss about the mixer design in RF circuits

Mixer Design in RF Circuits

Mixers are fundamental components in RF (Radio Frequency) circuits, widely used for
frequency translation, a critical function in both transmitters and receivers. They enable the
conversion of signals from one frequency to another, which is essential for signal processing
in communication systems, radars, and other RF applications. The design of mixers in RF
circuits involves several considerations, including linearity, noise performance, isolation,
conversion gain or loss, and power consumption. This discussion will explore the different
types of mixers, their design principles, and key performance criteria relevant to RF circuits.

Types of Mixers in RF Circuits

Mixers in RF circuits can be broadly categorized into passive mixers and active mixers,
each with distinct characteristics and design considerations.

1. Passive Mixers

Passive mixers use non-linear passive components, such as diodes or field-effect transistors
(FETs) operating as switches, to achieve mixing. They do not provide gain and typically have
a conversion loss.

 Diode Mixers: Use diodes arranged in configurations such as single-ended, single-

balanced, or double-balanced. They rely on the non-linear I-V characteristics of
diodes to produce the mixing products.
o Advantages: High linearity, wide bandwidth, simple design, and high power-
handling capability.
o Disadvantages: Conversion loss (typically 5-10 dB), high LO (Local
Oscillator) drive requirements, and poor noise figure.

 Switch Mixers: Utilize FETs or MOSFETs acting as switches controlled by the LO

signal.
o Advantages: Lower LO drive requirements compared to diode mixers, good
linearity, and integrability with CMOS technology.
o Disadvantages: Still exhibit conversion loss and require careful control of LO
drive levels for optimal performance.

21
2. Active Mixers

Active mixers use active devices like BJTs or MOSFETs that provide both mixing and
amplification, which results in conversion gain rather than conversion loss.

 Gilbert Cell Mixer: The most common active mixer design, consisting of a
differential amplifier followed by a double-balanced switching quad.
o Advantages: Provides conversion gain, low noise figure, good linearity, high
port isolation, and is easily integrable in CMOS and bipolar technologies.
o Disadvantages: Higher power consumption and complexity compared to
passive mixers.

 Single-Balanced and Double-Balanced Mixers:

o Single-Balanced Mixers: Use one or two transistors to perform the mixing
operation. They provide moderate LO-to-RF isolation and are simpler to
design.
o Double-Balanced Mixers: Use a quad of transistors in a balanced
configuration to suppress both the LO and RF feedthrough to the output,
providing excellent port-to-port isolation and better suppression of even-order
harmonics.

Key Design Considerations for Mixers in RF Circuits

When designing mixers for RF circuits, several performance criteria must be considered to
ensure optimal functionality and performance in the target application. The following are the
key design considerations:

1. Conversion Gain or Loss

o Conversion Gain: In active mixers, conversion gain is a desirable
characteristic as it amplifies the desired signal while performing frequency
conversion, improving the signal-to-noise ratio (SNR) and reducing the overall
noise figure of the receiver.
o Conversion Loss: Passive mixers typically exhibit a conversion loss, where
the output signal is weaker than the input RF signal. This needs to be
compensated for in subsequent stages of the RF chain.

2. Linearity and Intermodulation Distortion

o Linearity: Mixers should maintain linearity to minimize distortion and
intermodulation products, especially when handling multiple signals or strong
input signals. Good linearity is critical in communication systems to avoid
interference and maintain signal integrity.
o Third-Order Intermodulation (IM3): The third-order intercept point (IP3) is
a key metric for assessing a mixer's linearity. A higher IP3 indicates better
linearity and lower distortion levels.

3. Noise Figure (NF)

o Noise Figure: The noise figure of a mixer impacts the overall noise
performance of an RF front-end, especially in receivers. Active mixers

22
 generally have a lower noise figure compared to passive mixers due to the
gain they provide, which amplifies the signal relative to the noise.

4. Port Isolation
o Port-to-Port Isolation: Good isolation between the RF, LO, and IF ports is
crucial to prevent leakage of signals from one port to another. This reduces
crosstalk and prevents unwanted mixing products from appearing at the
output. Double-balanced mixers typically offer better isolation than single-
balanced or passive mixers.

5. LO Drive Level
o LO Drive Requirements: The local oscillator's drive level is an important
consideration in mixer design. Passive mixers often require higher LO drive
levels (10-20 dBm) to ensure proper diode or switch operation, while active
mixers can operate with lower LO levels due to the gain provided by the active
devices.

6. Bandwidth and Frequency Range

o Operational Bandwidth: The mixer's design should accommodate the desired
operational bandwidth and frequency range. Wideband mixers are required for
applications involving multiple frequency bands or wideband signals, such as
in software-defined radios (SDRs) and multi-band receivers.
o Frequency Range: The choice of mixer topology and components should
match the target frequency range of operation, whether for low-frequency IF,
microwave, or millimeter-wave applications.

7. Power Consumption
o Power Efficiency: Active mixers consume more power than passive mixers
due to the biasing of active devices. Power consumption should be minimized,
especially in battery-operated or portable devices.

8. Size and Integration

o Integration with IC Technology: Mixers should be designed for easy
integration with other RF components in an IC. The choice of technology
(CMOS, SiGe, GaAs, etc.) impacts the design, performance, and integration
density.

Typical Mixer Design Examples in RF Circuits

To illustrate the design principles, here are a few typical mixer designs:

1. CMOS Gilbert Cell Mixer

A CMOS Gilbert cell mixer is a common design for RFICs due to its ease of integration in
standard CMOS technology.

 Design Features:
o Uses CMOS transistors for both the differential amplifier stage and the
switching quad.

23
 o Provides conversion gain, low noise figure, and high port isolation.
o Suitable for low-power applications and offers good linearity.

 Applications: Widely used in RF receivers and transmitters for mobile

communication, WLAN, and GPS due to its integrability and performance.

2. Diode Ring Mixer

A diode ring mixer is a classic example of a passive mixer used in RF circuits.

 Design Features:
o Utilizes four diodes in a ring configuration with a balanced transformer at the
input and output.
o Provides high linearity and wide dynamic range but with conversion loss and
high LO drive requirements.
o High isolation between ports due to the balanced configuration.

 Applications: Used in RF front-ends, radar systems, and high-power applications

where robustness and linearity are essential.

3. FET-Based Passive Mixers

FET-based mixers use field-effect transistors (such as MOSFETs) as switches controlled by

the LO signal.

 Design Features:
o Lower LO drive requirements compared to diode mixers.
o Good linearity and integration capabilities with CMOS technology.
o Moderate conversion loss and noise figure.

 Applications: Suitable for low-power RF applications, SDRs, and multi-band

receivers.

Conclusion

Mixer design in RF circuits involves a trade-off between various performance metrics such as
conversion gain or loss, noise figure, linearity, isolation, and power consumption. The choice
between active and passive mixers depends on the specific requirements of the application,
including frequency range, bandwidth, power constraints, and integration considerations.
Understanding these design principles and trade-offs is essential for optimizing mixer
performance in RFICs and ensuring the efficient operation of wireless communication
systems, radar, and other RF applications.

7(a) Explain about Quartz crystal resonators with suitable diagram

Quartz crystal resonator basics

Quartz crystal resonator technology relies on the remarkable properties of quartz for its
operation. When placed into an electronic circuit a quartz crystal acts as a tuned circuit.
However it has an exceptionally high Q.

24
Ordinary LC tuned circuits may exhibit values of a few hundred if carefully designed and
constructed, but quartz crystals exhibit values of up to 100 000.
Apart from their Q, crystal technology also has a number of other advantages. They are very
stable with respect to temperature and time. In fact most crystals will have these figures
specified and they might typically be ±5 ppm (parts per million) per year for the ageing and
±30 ppm over a temperature range of 0 to 60 °C.

Then the Q-factor of our crystal example, about 25,000, is because of this high XL/R ratio.
The Q-factor of most crystals is in the area of 20,000 to 200,000 as compared to a good LC
tuned tank circuit we looked at earlier which will be much less than 1,000. This high Q-factor
value also contributes to a greater frequency stability of the crystal at its operating frequency
making it ideal to construct crystal oscillator circuits.
So we have seen that a quartz crystal has a resonant frequency similar to that of a electrically
tuned LC tank circuit but with a much higher Q factor. This is due mainly to its low series
resistance, Rs. As a result, quartz crystals make an excellent component choice for use in
oscillators especially very high frequency oscillators.
Typical crystal oscillators can range in oscillation frequencies from about 40kHz to well over
100MHz depending upon their circuit configuration and the amplifying device used. The cut
of the crystal also determines how it will behave as some crystals will vibrate at more than
one frequency, producing additional oscillations called overtones.
Also, if the crystal is not of a parallel or uniform thickness it may have two or more resonant
frequencies both with a fundamental frequency producing what are called and harmonics,
such as second or third harmonics.
Generally though the fundamental oscillating frequency for a quartz crystal is much more
stronger or pronounced than that of and secondary harmonics around it so this would be the
one used. We have seen in the graphs above that a crystals equivalent circuit has three
reactive components, two capacitors plus an inductor so there are two resonant frequencies,
the lowest is a series resonant frequency and the highest is the parallel resonant frequency.
We have seen in the previous tutorials, that an amplifier circuit will oscillate if it has a loop
gain greater or equal to one and the feedback is positive. In a Quartz Crystal
Oscillator circuit the oscillator will oscillate at the crystals fundamental parallel resonant
frequency as the crystal always wants to oscillate when a voltage source is applied to it.
However, it is also possible to “tune” a crystal oscillator to any even harmonic of the
fundamental frequency, (2nd, 4th, 8th etc.) and these are known generally as Harmonic
Oscillators while Overtone Oscillators vibrate at odd multiples of the fundamental
frequency, 3rd, 5th, 11th etc). Generally, crystal oscillators that operate at overtone
frequencies do so using their series resonant frequency.

Colpitts Quartz Crystal Oscillator

Crystal oscillator circuits are generally constructed using bipolar transistors or FETs. This is
because although operational amplifiers can be used in many different low frequency
(≤100kHz) oscillator circuits, operational amplifiers just do not have the bandwidth to
operate successfully at the higher frequencies suited to crystals above 1MHz.
The design of a Crystal Oscillator is very similar to the design of the Colpitts Oscillator we
looked at in the previous tutorial, except that the LC tank circuit that provides the feedback
oscillations has been replaced by a quartz crystal as shown below.

25
Colpitts Crystal Oscillator

This type of Crystal Oscillators are designed around a common collector (emitter-follower)
amplifier. The R1 and R2 resistor network sets the DC bias level on the Base while emitter
resistor RE sets the output voltage level. Resistor R2 is set as large as possible to prevent
loading to the parallel connected crystal.
The transistor, a 2N4265 is a general purpose NPN transistor connected in a common
collector configuration and is capable of operating at switching speeds in excess of 100Mhz.
The circuit diagram above of the Colpitts Crystal Oscillator circuit shows that
capacitors, C1 and C2 shunt the output of the transistor which reduces the feedback signal.
Therefore, the gain of the transistor limits the maximum values of C1 and C2. The output
amplitude should be kept low in order to avoid excessive power dissipation in the crystal
otherwise could destroy itself by excessive vibration.

Key Components and Operation

1. Colpitts Oscillator Basics:

o The Colpitts oscillator is an LC oscillator configuration that uses a capacitive
voltage divider network (typically two capacitors) to provide the necessary
feedback for oscillation.
o The capacitors C1 and C2 are connected in series and form a voltage divider
network. The junction of these capacitors is typically connected to the
transistor's base or gate (depending on whether a bipolar junction transistor
(BJT) or field-effect transistor (FET) is used).
o An inductor L is connected in parallel with the capacitor network, forming a
resonant LC circuit that determines the oscillator's frequency.

2. Quartz Crystal:
o A quartz crystal is a piezoelectric device that vibrates at a precise frequency
when an AC voltage is applied to it. This frequency is determined by the cut
and size of the crystal.
o The crystal provides high frequency stability and low phase noise, making it
an excellent choice for applications where precision is crucial.
o In the Colpitts oscillator circuit, the quartz crystal can be used either as a
series or parallel resonant element to set or stabilize the oscillator frequency.

3. Circuit Operation:
o The transistor (BJT or FET) in the circuit acts as an amplifier. It amplifies the
small feedback signal from the capacitive voltage divider and sustains
oscillations.
o The LC network (or the quartz crystal) sets the oscillator's frequency. In the
crystal-controlled version, the crystal dominates the frequency-determining
mechanism, providing stability.

26
 o The feedback signal from the capacitive divider network must be in phase with
the original signal to sustain oscillations. The circuit is designed such that the
phase shift around the loop is 360 degrees (or 0 degrees) to satisfy the
Barkhausen criterion for sustained oscillations.

 R1: Base bias resistor

 C1, C2: Capacitors forming a voltage divider network
 Q: Transistor (BJT or FET) used as an active amplifying device
 L: Inductor (optional, depending on whether the crystal alone sets the frequency or an
LC network is used)

Advantages of Colpitts Quartz Crystal Oscillators

1. High Stability: The use of a quartz crystal provides excellent frequency stability over
temperature and time.
2. Low Phase Noise: The circuit provides a clean signal with low phase noise, which is
essential in communication systems.
3. Simplicity: The Colpitts configuration is simple to design and implement, making it
popular for various RF and IF applications.

Applications

 RF Signal Generation: Used in RF transmitters and receivers for generating stable

carrier signals.
 Clock Generation: Employed in digital circuits and microcontrollers to provide a
precise clock signal.
 Frequency Synthesizers: Used in conjunction with PLLs (Phase-Locked Loops) to
generate a range of frequencies.
 Communication Systems: Essential in radio, television, and other communication
systems for stable frequency generation.

Conclusion

A Colpitts Quartz Crystal Oscillator combines the benefits of the Colpitts oscillator topology
with the precision of a quartz crystal, making it a robust choice for high-frequency and high-
stability applications. The circuit is simple yet highly effective, ensuring reliable performance
in a wide range of electronic applications.

7(b) Describe phase noise considerations in synthesizer

27
Phase Noise Considerations in RF Synthesizer Design

Phase noise is a critical parameter in RF synthesizer design, especially for applications

involving frequency modulation, digital communication systems, radar, and other sensitive
RF applications. Phase noise refers to the short-term, random fluctuations in the phase of a
signal, which manifest as noise sidebands around the carrier frequency. In a frequency
synthesizer, phase noise can degrade the performance of the entire system, affecting signal
purity, data integrity, and overall spectral efficiency.

What is Phase Noise?

 Phase Noise: Phase noise is defined as the noise spectrum that appears around a
carrier frequency due to phase fluctuations. It is usually measured in decibels relative
to the carrier (dBc) per hertz of bandwidth at a certain frequency offset from the
carrier.
 Impacts of Phase Noise:
o Signal Integrity: Phase noise affects the signal-to-noise ratio (SNR) and can
lead to errors in digital communication systems.
o Adjacent Channel Interference: High phase noise can cause interference in
adjacent channels, reducing the effectiveness of frequency planning in
communication systems.
o Radar Performance: In radar systems, phase noise can degrade range
resolution and target detection capability.

Sources of Phase Noise in Synthesizers

1. Voltage-Controlled Oscillator (VCO) Noise:

o The VCO is a critical component of an RF synthesizer, and its phase noise
characteristics significantly influence the overall phase noise of the
synthesizer.
o VCO phase noise is primarily due to thermal noise in active components (like
transistors) and flicker noise (1/f noise).

2. Phase-Locked Loop (PLL) Noise:

o The PLL circuit in a synthesizer introduces noise due to the phase detector,
loop filter, and charge pump.
o The noise from the PLL components contributes to the synthesizer's overall
phase noise, especially at close-in offsets from the carrier frequency.

3. Reference Oscillator Noise:

o The reference oscillator, typically a crystal oscillator, introduces its own phase
noise. This noise is particularly noticeable at low offset frequencies.
o The PLL design can amplify this reference noise, depending on the loop
bandwidth and the multiplication factor used in the synthesizer.

4. Digital Noise:
o In fractional-N synthesizers, digital components like delta-sigma modulators
can introduce quantization noise. This noise can alias back into the baseband
and cause phase noise spurs.

28
Key Phase Noise Considerations in Synthesizer Design

1. Loop Bandwidth:
o The loop bandwidth of the PLL determines the trade-off between reference
oscillator noise and VCO noise.
o A narrow loop bandwidth suppresses reference oscillator noise effectively but
may allow VCO noise to dominate at frequencies beyond the loop bandwidth.
o A wide loop bandwidth can suppress VCO noise close to the carrier but might
introduce more reference noise into the output.

2. VCO Design:
o The VCO design directly impacts phase noise. Low-noise VCOs are typically
designed with high-Q resonant elements (e.g., LC tanks) and low-noise active
components.
o Differential design techniques and good layout practices can help minimize
the noise contribution from the VCO.

3. Charge Pump and Loop Filter Design:

o The charge pump and loop filter affect the noise transfer characteristics of the
PLL.
o Proper design of the charge pump current levels and loop filter components
(resistors, capacitors) is critical to minimize noise and spurs.
o Active loop filters might introduce additional noise but provide better control
over phase noise at lower frequencies.

4. Reference Oscillator Quality:

o The quality of the reference oscillator (often a high-stability crystal oscillator)
significantly affects the phase noise at low offset frequencies.
o A high-quality reference oscillator with low phase noise ensures better overall
synthesizer performance, especially at close-in frequency offsets.

Techniques for Minimizing Phase Noise

1. Optimize Loop Filter Design:

o Carefully design the loop filter to balance noise contributions from different
sources. A well-designed filter can effectively suppress phase noise from the
reference oscillator and VCO.

2. Use High-Quality Components:

o Select low-noise components for critical paths, such as high-Q inductors and
capacitors for the VCO, low-noise amplifiers, and high-quality reference
oscillators.

29
 Practical Implications in RF Applications

 Communications Systems: In cellular networks, phase noise affects modulation

accuracy, data throughput, and the ability to maintain multiple connections in a
crowded RF environment.
 Radar Systems: In radar, low phase noise is essential for accurate target detection
and velocity measurement. High phase noise can lead to poor range resolution and
clutter.
 Signal Generators: For signal generators used in testing and measurement, phase
noise dictates the purity of the generated signal, affecting the accuracy of
measurements.

Conclusion

Phase noise is a critical consideration in RF synthesizer design that directly impacts system
performance across various applications. By carefully designing the PLL, selecting
appropriate components, and optimizing circuit parameters, engineers can minimize phase
noise and ensure robust, high-performance RF systems.

8 State the principle of operation of a basic negative resistance oscillator with

Schematics

Negative Resistance Oscillator Circuit

AuthorCADENCE PCB SOLUTIONS
Key Takeaways

 The negative differential resistance property generates oscillations in oscillator circuits

utilizing elements such as tunnel diodes, IMPATT diodes, TEDs, and negative impedance
converters.

30
 The negative resistance component cancels the positive resistance of the resonant circuit
and generates steady oscillations.
 The transistor in the negative resistance oscillator circuit should be in an unstable condition
to utilize its negative resistance region.

The oscillator uses a tunnel diode to form a negative resistance oscillator circuit

Most engineers know the famous Ohm’s law, but few are aware of its exceptions; cases in
which voltage and current are inversely proportional to each other and can be considered an
instance of negative resistance property.

The negative resistance property is of great use in communication systems, especially in

oscillator circuits employed in radio receivers, transmitters, signal generators, frequency
counters, network analyzers, etc. The oscillators that utilize the negative resistance property
of electronic components can be generalized as negative resistance oscillator circuits, and
these circuits can be implemented in different ways.

Negative Resistance Explained

As the voltage applied across the element in positive resistance circuits increases, there is an
increase in current and vice versa. However, certain electronic elements exhibit negative
resistance. In such elements, the current tends to decrease when voltage increases and vice
versa.

31
Common Elements Showcasing Negative Resistance Property

Element Reason for Negative Resistance

Tunnel Diode Quantum tunneling effect

Impact Ionization Avalanche Transit-

Avalanche multiplication process
Time (IMPATT ) Diode

Transferred Electron Device (TED) or Interaction between moving electron

Gunn Diode cloud and electric field

Negative Impedance Converter The help of transistors or op-amps

Negative resistance region in the V-I curve

In the voltage-current curve of negative resistance devices (shown above), there is a negative
resistance region where the current decreases with increasing applied voltage. Before and
after the negative resistance region, devices behave as positive resistance. By operating in
the negative resistance region, it is possible to build oscillator circuits using these devices
even without a positive feedback loop.

The negative resistance oscillator circuit generates sustained oscillations without a feedback
loop. The negative differential resistance property generates oscillations in the oscillator
circuits utilizing elements such as a tunnel diode, IMPATT diode, TED, negative impedance
converter, etc.
The product of voltage and current in the negative resistance oscillator circuit is negative
when the tunnel diode, IMPATT diode, TED, etc. operates in the negative resistance region
and leads to power generation. The damping limitation of conventional oscillators is also
eliminated by utilizing negative resistance oscillator circuits.

32
 Block Diagram of Negative Resistance Oscillator Circuit

Block diagram of a negative resistance oscillator circuit

1. Negative resistance component - The negative resistance element can be two-terminal devices
such as tunnel diodes, IMPATT, Gunn diodes, UJT, or three-terminal transistors like MESFETs.
Two NPN transistors connected in a push-pull configuration or as differential pairs form a
negative resistance network. The two-terminal devices are polarized to operate as negative
resistance, whereas a feedback network is required for three-terminal devices to operate in
the negative resistance mode.
2. Resonant circuit - Frequency selection is made with the help of a resonant circuit. A parallel
combination of resistor, capacitor, and inductor is an example of a commonly used resonant
circuit.
3. Load - Oscillation appears across the load. There can be transition circuits included between
the source and the load to improve the performance of the oscillator.

33