i

“Implementation of Mixer using any two Analog Signals”

A Hardware project report

Submitted by

B-Tech Vth

Semester, Electronics and Communication

Under the guidance of

Asim Mukherjee Assistant Professor

Department of Electronics and Communication Engineering

Motilal Nehru National Institute of Technology

Allahabad-211004

Anubhav Srivastava – 20083019

Ravi Jain – 20085063

Tushar Garg – 20082039

Vikram Singh – 20083005

ii

MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY

Department of Electronics and Communication Engineering

Allahabad-211004

Certificate

This is to certify that the hardware project titled “Implementation of Mixer using any two Analog

Signals” submitted by Anubhav Srivastava, Ravi Jain, Tushar Garg, Vikram Singh to the

Electronics And Communication Engineering Department, Motilal Nehru National Institute of

Technology(Deemed University), Allahabad, is a bonafide work of students carried out under my

supervision.

Date: 20-11-2010 Asim Mukherjee

Place: Allahabad Assistant Professor

iii

Acknowledgement

It is a great privilege for us to express our deep sense of gratitude to our supervisor Asim

Mukherjee of ECE department, MNNIT Allahabad for his stimulating guidance and

profound assistance. We shall always cherish our association with him for his constant

encouragement and freedom to thought and action that he rendered to us throughout our

hardware project. We also feel a great pleasure to thank all the staff members of the

department for their cooperation which led to the successful completion of our work.

Finally, it is a great pleasure to thank one and all who helped us in carrying out this

project.

Date: 21-11-2010

Place: Allahabad

Anubhav Srivastava (20083019)

Tushar Garg (20082039)

Ravi Jain (20085063)

Vikram Singh (20083005)

vi

Contents

Title Page

CERTIFICATE………………………………………………………………………………………….ii

ACKNOWLEDGEMENT………………………………………………………………………….......iii

ABSTRACT……………………………………………………………………………………………...iv

CONTENTS……………………………………………………………………………...…………...….v

CHAPTER 1 Introduction

1.1 Need of Mixer……………………………………………………….…………….2

1.2 Mixer...............................................................................................................…...2

1.3 Concept of ideal mixer…………………………………………………...............2

1.4 Implementation of mixer by various methods……………………………………4

1.5 Mixer using Diodes……………………………………………………………….5

1.6 Transdiode-Basic Concept………………………………………………………..6

CHAPTER 2 Theoretical Background

2.1 Mixers….………………………………..……………………………...…………8

2.2 Mixer: A Mathematical Approach…………………….………………………….9

2.3 Mixer Terminology………………………………………………………………10

2.4 Important Mixer Designs and Problems Concerned……………………………..11

2.4.1 Gilbert Cell………………….……………………………………………12

2.4.2 Single Ended Diode Mixer…………………………………………...….12

2.4.3 Single balanced diode Mixer…………………………………………….13

2.4.4 Double balanced diode Mixer…………………………………………....13

2.4.5 FET Mixer………………………………………………………………..14

CHAPTER 3 Approach Used Towards Mixer Design: Transdiode and OP-Amps

3.1 Need of OP-Amps……………………………………………………………….16

vi

3.2 Log and Anti Log Converters………………………………………………….16

3.2.1 Log Converters…………….………..………………………………….16

3.2.2 Anti Log Converters.…………………………………………………...17

3.3 First Order Low Pass Filter…………………………………………………….19

3.4 Result…………………………………………………………………………..21

CHAPTER 4 ANALYSIS AND DISCUSSION

4.1 Overall Analysis of Mixer…….………………………………………………..23

4.2 Existing Problems………………………….…………………………………..25

4.3 Discussions…….………………………………………………………………26

REFERENCES………………………………………………………………..…………………….…..29

1

Chapter 1

Introduction

2

1.1 Need of Mixer

In any communication or electrical system, frequency of the signal at which it is being processed is of

most importance. Often very high frequency is selected for transmission of the signal, because lower

the frequency, lesser is the distance it can travel before it gets attenuated too much, or get corrupted by

noise. Higher the frequency, lesser is the attenuation, which means, higher the frequency, greater is the

distance which the wave can reach with reasonable attenuation levels.

This is the reason we modulate baseband signals to high frequencies in radio communication, it’s also

the reason for the use of very high frequencies in case of satellite communications. But having very

high frequency also has some disadvantage. At very high frequencies (gigahertz), signal processing

circuitry performs poorly. Active devices such as transistors cannot deliver much amplification (gain)

without becoming unstable. Ordinary circuits using capacitors and inductors must be replaced with

cumbersome high frequency techniques such as striplines and waveguides. So a high frequency signal

is converted to a lower Intermediate Frequency (IF) for processing. Hence, depending upon the

processing to be performed, frequency of the signals is often required to up or down converted (mostly

down conversion). This frequency translation is achieved using device known as MIXER.

1.2 Mixer

Mixers are frequency translation devices. They allow the conversion of signals between a high

frequency (the RF frequency) and a lower Intermediate Frequency (IF) or baseband. In

communications systems the RF is the transmission frequency, which is converted to an IF to allow

improved selectivity (filtering) and an easier implementation of low noise and high gain amplification.

It is a nonlinear or time-varying circuit or device that accepts as its input two different frequencies and

presents at its output a mixture of signals at several frequencies:

1. The sum of the frequencies of the input signals

2. The difference between the frequencies of the input signals.

3. Unwanted intermodulation products from the inputs

• Both original input frequencies — these are often considered parasitic and are filtered out

in the subsequent filter stages.

• A balanced mixer passes only a small leakage of the original signal to the output, often

implemented as a double balanced mixer which has high isolation of both inputs.

1.3 Concept of Ideal Mixer

An ideal mixer multiplies two input signals and the output signal contains the frequency terms of both

3

the input signals as well as the sum and difference of two frequencies. A block diagram representation

of an ideal mixer is shown in figure1.1.

Fig.1.1 Block diagram of an ideal mixer

Suppose the two input signals are sinusoidal signals with frequencies f1 and f2 as shown in fig. 1.2(a)

and 1.2(b). The output signal of an ideal mixer will have a frequency as sum and difference of two

frequencies as shown in fig.1.2(c).

Fig.1.2 (a) Input signal 1 with f1=2000Hz

Fig.1.2 (b) Input signal 2 with f2=2200Hz

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

4

Fig.1.2(c) Output signal with f1-f2=200Hz and f1+f2=4200Hz

In this example two input signals are

f1(t) = sin (2πf1t)

f2(t) = sin (2πf2t)

On feeding to the mixer the output g(t) is obtained

g(t) = f1(t).f2(t)

g(t) = 1

2[Cos (2π (f1-f2) t) - Cos(2π(f1+f2) t)]

So the output obtained has two frequency components f1-f2 and f1+f2.

1.4 Implementation of Mixer by various methods

In this project the mixer circuit is implemented using the concept of transdiodes which is similar in

working to a diode but gives better practical results. For frequency translation (either up conversion or

down conversion) it is required to multiply two signals having different frequencies. This can be done

in number of ways as

1. Gilbert Cell

2. Single Ended Diode Mixer

3. Single Balanced Diode Mixer

4. Double Balanced Diode Mixer

5. FET Mixer

A detailed description of each type of mixer is given in chapter 2.

0.002 0.004 0.006 0.008 0.01

-1

-0.5

0.5

1

1.1

1.2

1.3

1.4

5

1.5 Mixer using Diodes

In this project the mixer is implemented using the concept of transdiode and Op-Amps. A mixer is

implemented by multiplying two signals. The multiplication is done using logarithmic circuit. When

two log terms are added the mantissa terms get multiplied. The same concept is used here. Logarithmic

converter uses non linear devices such as diodes or transistors. The equation for a diode can be

approximated by Eqn (1.5).

I=I0(𝑒−𝑞𝑉

𝑘𝑇 − 1)

where

I is the current flowing through the diode

V is voltage across the diode

k is the Boltzmann’s constant

q is the electron charge

Io is the reverse diode leakage current

T is the absolute temperature

Fig 1.3 Basic Log converter circuit

Applying the equation 1.5 to the circuit given in Fig 1.3 gives

Iin=𝑉𝑖𝑛

𝑅1I0(𝑒−

𝑞𝑉𝑜𝑢𝑡

𝑘𝑇 − 1)

Vout=𝑘𝑇

𝑞log𝑒(

𝑉𝑖𝑛

𝑅1∙𝐼𝑜+ 1)

For building practical logarithmic amplifiers, transistors are usually preferred over diodes, as shown in

the transdiode logarithmic amplifier circuit of Fig. 1.4 using a grounded base npn transistor in the

feedback loop when the input is positive. In this circuit several drawbacks of diode circuit are removed

as listed below:

1. Its response is very temperature sensitive (note the T and Io terms in the transfer equation).

2. Diodes do not provide a good log conformity, which means that the relationship between their

forward voltage and their current does not accurately follow a logarithmic form.

1.5

1.6

1.7

6

1.6 Transdiode – Basic Concept

Transistors, however, provide a far better conformity than diodes. Many general purpose transistors

configured as diodes can provide good logging of up to seven decades of magnitude of input current.

The bipolar transistor offers this best performance due to the fact that its conduction is based upon

majority carrier, either electrons or holes, whereas diode conducts with both electrons and holes. The

relationship between the collector current and the base-emitter voltage, with the base-collector voltage

at 0 V, is given in eqn. 1.8 as shown in Fig. 1.4.

Fig. 1.4 Transdiode

Ic = Is (𝑒𝑞𝑉

𝑘𝑇 − 1)

So the logarithmic circuit can also be implemented using transdiode. A detailed report of log converter

using transdiodes and Op-Amps is given in chapter 3.

1.8

7

Chapter 2

Theoretical Background

8

2.1 Need of Mixer

Mixers are used for frequency conversion and are critical components in modern radio frequency (RF)

systems. A mixer converts RF power at one frequency into power at another frequency to make signal

processing easier and also inexpensive. A second reason to use an intermediate frequency (IF), in

receivers that can be tuned to different stations, is to convert the various different frequencies of the

stations to a common frequency for processing. It is difficult to build amplifiers, filters, and detectors

that can be tuned to different frequencies, but easy to build tuneable oscillators. Superheterodyne

receivers tune in different stations simply by adjusting the frequency of the local oscillator on the input

stage, and all processing after that is done at the same frequency, the IF. Without using an IF, all the

complicated filters and detectors in a radio or television would have to be tuned in unison each time

the station was changed, as was necessary in the early tuned radio frequency receivers.

But the main reason for using an intermediate frequency is to improve frequency selectivity. In

communication circuits, a very common task is to separate out or extract signals or components of a

signal that are close together in frequency. This is called filtering. Some examples are, picking up a

radio station among several that are close in frequency, or extracting the chrominance subcarrier from

a TV signal. With all known filtering techniques the filter's bandwidth increases proportionately with

the frequency. So a narrower bandwidth and more selectivity can be achieved by converting the signal

to a lower IF and performing the filtering at that frequency.

Perhaps the most commonly used intermediate frequencies are around 455 kHz for AM receivers and

10.7 MHz for FM receivers. However, the intermediate frequency can range from 10–100 MHz

Intermediate frequency (IF) are generated by mixing the RF and LO frequency together to create a

lower frequency called IF. Most of the ADC/DAC operates in low sampling rates, so input RF must be

mixed down to IF to be processed.

Table 2.1 Commonly used intermediate frequencies

Application Frequency Remarks

Television

receivers

30 MHz to 900 MHz

Analogue

television

receivers using

system M

41.25 MHz (audio) and

45.75 MHz (video).

The channel is flipped over in the conversion

process in an intercarrier system, so the audio

IF frequency is lower than the video IF

frequency. Also, there is no audio local

oscillator; the injected video carrier serves that

purpose.

9

FM radio

receivers

262 kHz,455 kHz,1.6 MHz,

5.5 MHz,10.7 MHz,10.8 MHz,

11.2 MHz,11.7 MHz,11.8 MHz,

21.4 MHz, 75 MHz and

98 MHz

In double-conversion super heterodyne

receivers, a first intermediate frequency of

10.7 MHz is often used, followed by a second

intermediate frequency of 470 kHz. There are

triple conversion designs used in police scanner

receivers, high-end communications receivers,

and many point-to-point microwave systems.

AM radio

receivers

450 kHz, 455 kHz, 460 kHz,

465 kHz, 470 kHz, 475 kHz,

480 kHz

Satellite uplink

downlink

equipment: 70 MHz, 950-1450

Downlink first IF

Terrestrial

microwave

equipment

250 MHz,70 MHz or 75 MHz

Radar 30 MHz

Intermediate frequency tends to be lower frequency range compared to the transmitted RF frequency.

However, the choices for the IF are most depending on the available components such as mixer, filters,

amplifiers and others that can operate at lower frequency.

2.2 Mixer: A Mathematical Approach

The ideal mixer, represented by figure 2.1, is a device which multiplies two input signals. If the inputs

are sinusoids, taken as

v1 (t) = A1 sin 2𝜋f1t

v2 (t) = A2 sin 2𝜋f2t

where each A is amplitude, each f is a frequency, and t represents time. (In reality even such simple

waves can have various phases, but that is not relevant here.)

fig. 2.1 Ideal Mixer design

Frequency translation as achieved by mixer is done by adding the two signal’s frequency. This can

done by multiplication of the two sinusoidal signals by virtue of the trigonometric relation :

V1

V2

2.1

2.2

10

𝒔𝒊𝒏 𝜶 ∙ 𝒔𝒊𝒏 𝜷 =𝟏

𝟐[ 𝒄𝒐𝒔 𝜶 − 𝜷 − 𝒄𝒐𝒔 𝜶 + 𝜷 ]

Using this relation, we obtain

where the sum (f1 + f2) and difference (f1 − f2) frequencies appear. Typically, either the sum, or the

difference, frequency is removed with a filter. Thus basis of most of the mixer design is the

implementation of signal multiplier.

2.3 Mixer Terminology

Listed below are some of the terms used in referring to mixers or mixing performance:

Conversion loss: The ratio of the wanted output signal level to the input, normally expressed

in decibels (dB). Conversion Gain or Loss of the RF Mixer is dependent by the type of the

mixer (active or passive), but is also dependent by the load of the input RF circuit as well the

output impedance at the RF port. The typical conversion gain of an active Mixer is

approximately +10dB when the conversion loss of a typical diode mixer is approximately -

6dB.

The Conversion Gain or Loss of the RF Mixer measured in dB is given by:

Conversion [dB] = Output IF power delivered to the load [dBm] – Available RF input signal Power [dBm]

Noise Figure: The ratio of the Signal to Noise Ratio (SNR) at the input compared to the SNR

at the output, measured at 290K.

Double Sideband (DSB) Noise Figure: Includes noise and signal contributions at both

the RF and the image frequencies.

Single Sideband (SSB) Noise Figure: No image signal is included although image noise

is included, provided the mixer performance is the same at the image and the wanted

frequencies,

Linearity. The linearity of a mixer refers to its signal level handling ability.

Input Intercept Point (IIP3): It is the RF input power at which the output power levels of

the unwanted intermodulation products and the desired IF output would be equal. The Third-

Order intercept point (IP3) in a Mixer is defined by the extrapolated intersection of the primary

IF response with the two-tone third-order intermodulation IF product that results when two RF

2.3

2.4

11

signals are applied to the RF port of the Mixer.

Fig. 2.2 IIP3- interpolation

Spurs: An abbreviation of spurious product. The term is used to describe any unwanted

mixing product. One way to reduce such products is to short-circuit the higher harmonics of the

LO at the intrinsic Mixer terminals to lower the power in such responses. Reducing the second

or third harmonic of the local oscillator reduces its harmonic products by 20 to 25 dB and 10 to

15 dB, respectively.

Sub-harmonic mixer. This is a mixer circuit designed to accept an LO input at a fraction

(often a half) of the desired LO mixing frequency.

Harmonic mixer: This is just another term for sub-harmonic mixer but is more commonly

used for circuits employing higher multiples of the input LO to produce the mixing LO.

Pump: It is used to describe the LO drive. The LO input is said to be ―pumping‖ the mixer.

Image frequency: For high side injection (FLO > FRF) this is FLO + FIF, for low side injection

(FLO < FRF) it is FLO - FIF. In down-convert mixers, it is a frequency that is converted directly to

IF along with the IF itself. In up-convert mixers it is an unwanted sideband which, without

additional filtering, is usually at a similar level to the wanted signal.

Image enhancement: A method for reducing the conversion loss of a mixer by terminating

the image frequency in appropriate reactive impedance.

2.4 Important Mixer Designs and Problems Concerned

Some very popular approach toward Mixer design is Gilbert Cell and the use of Non-Linear devices

such as Diodes, FETs.

12

2.4.1 Gilbert Cell: The Gilbert cell uses a linear, time-varying circuit to achieve time-domain

multiplication, and hence, frequency shifting. A Gilbert cell is shown in fig. 2.2. The RF signal is input

to a long-tailed differential amplifier. The collectors of Q1 and Q2 have a cross connected set of four

transistors, which are driven by a local oscillator (LO). It uses the local oscillator (LO) to flip the

polarity of the radio-frequency (RF) input. When the LO is positive, the RF input passes to the

intermediate-frequency (IF) output without being reversed. When the LO is negative, the RF input is

reversed as it passes to the IF output. So, the LO "flips" the polarity of the RF signal. This has the

effect of multiplying by +1 or 1 (neglecting losses).

Fig 2.3 Gilbert Cell

2.4.2 Single ended Diode Mixer: Such Mixers, which utilise a single diode as the mixing element,

have no inherent isolation between the mixer ports and are known as single-ended designs. Fig 2.4

shows a basic block diagram of a single-ended mixer.

Fig 2.4 Basic Block of Single ended diode mixer

One of the main difficulties with single-ended designs is that the LO and RF inputs must be separated

with a diplexer filter. They are normally relatively closely spaced and separating the two frequency

bands can be problematic. Coupled with this, the fact that no inherent spurious suppression is afforded

13

by this topology, it is not surprising that few modern diode mixer designs are single-ended. The

exception to this is high mm-wave frequency designs, which are still often realised with a single diode.

2.4.3 Single balanced Diode Mixer: A single-balanced diode mixer uses two diodes. Either the

LO drive or the RF signal is balanced (applied in anti-phase), adding destructively at the IF port of the

mixer and providing inherent rejection. The level of rejection is dependent on the matching between

the two diodes. A rejection of 20 to 30dB is normally possible for good discrete designs. Other

advantages of a singly-balanced design are rejection certain mixer spurious products, depending on the

exact configuration and suppression of Amplitude Modulated (AM) LO noise.

One disadvantage of balanced designs is that they require a higher LO drive level. Figure 2.5 shows a

block diagram of a single-balanced mixer. It utilises an anti-phasal diode pair. Matched diode pairs, in

various configurations, are readily available in low-cost plastic packages.

Fig. 2.5 Basic Block Diagram of a single balanced mixer

For the topology shown in Figure 2.5, the LO drive to the two diodes is in anti-phase (balanced) and the RF

signal is in-phase. If the mixing products are at mRF ± nLO, this mixer will reject all products where m is even.

If the RF drive were in anti-phase and the LO in-phase, all spurious products with n even would be rejected. The

anti-phase signal is also cancelled at the IF port. Because the LO drive should be at a significantly higher level

than the RF signal, it is often chosen as the anti-phase signal to increase the LO to IF isolation.

2.4.4 Double-balanced Diode Mixers: A double-balanced diode mixer normally make use of

four diodes in a ring or star configuration with both the LO and RF being balanced. All ports of the

mixer are inherently isolated from each other. The advantages of a double-balanced design over a

single balanced design are increased linearity, improved suppression of spurious products (all even

order products of the LO and/or the RF are suppressed) and the inherent isolation between all ports.

The disadvantages are that they require a higher level LO drive and require two baluns. A balun is a

type of electrical transformer that can convert electrical signals that are balanced about ground

14

Fig: 2.6 Block diagram for doubly-balanced diode Mixer

(Differential) to signals that are unbalanced (single-ended) and vice versa. They are also often used to

connect lines of differing impedance. Figure 9 shows a block diagram of a double-balanced quad-ring

diode mixer.

2.4.5 FET Mixers: FETs can be used in mixers in both active and passive modes. Active FET

mixers are transconductance mixers using the LO signal to vary the transconductance of the transistor.

Figure 2.7 shows the simplest realisation of a transconductance mixer, biasing circuitry has been

omitted for clarity. The RF (and LO) short circuit at the drain is important to ensure that the value of

Fig 2.7 Simple Transconductance Mixer

Vds is not moved significantly from its DC bias point by the applied LO. This ensures the magnitude of

the time varying transconductance is maximised so optimising the conversion gain. Unfortunately it

also means that this mixer topology is not well suited to realising upconverters. This topology has the

disadvantage that some form of diplexing is required to separate the RF and LO inputs which are

incident on the same port. A diplexer is a passive device that implements frequency domain

multiplexing.

15

Chapter 3

Approach Used Towards Mixer

Design: Transdiode and OP-Amps

16

3.1 Need of OP-Amps

As discussed in 2.2, frequency shifting/mixing can be achieved by multiplying two given signals in

time domain. This signal multiplication can be easily converted into addition and subtraction process

using logarithmic and antilogarithmic property, which is as given as

log 𝑥 ∙ 𝑦 = log 𝑥 + log 𝑦

𝑥 = 𝑒 log (𝑥)

Thus basis of our approach toward mixer design is the design of multiplier circuit consisting of log and

antilog circuits. These log anti-log converters has been designed using OP-Amps and thus it simplifies

our mixer’s theoretical background.

fig 3.1 Basic Block diagram of Multiplier Circuit

3.2 Log and Antilog Converters

Log and antilog converters use the exponential property of a forward biased p-n junction, using a

bipolar transistor, to provide the necessary log or antilog function.

3.2.1 Log Converters:

The simplest design of a log converter is as shown in fig 3.2. It has major drawbacks including very

poor log conformity and drifting of the output due to temperature variations. Although this circuit is

very rarely used, it does provide a good starting point from which more practical log converter (which

has been implemented in this project) designs can easily be developed.

The equation for a diode can be approximated by

I=I0(𝑒−𝑞𝑉

𝑘𝑇 − 1)

where

I is the current flowing through the diode

3.1

3.2

3.3

17

V is voltage across the diode

k is the Boltzmann’s constant

q is the electron charge

Io is the reverse diode leakage current

T is the absolute temperature

Fig 3.2 Basic Log converter circuit

Applying the equation 1.5 to the circuit given in Fig 3.2 gives

Iin=𝑉𝑖𝑛

𝑅1I0(𝑒−

𝑞𝑉𝑜𝑢𝑡

𝑘𝑇 − 1)

Vout=𝑘𝑇

𝑞log𝑒(

𝑉𝑖𝑛

𝑅1∙𝐼𝑜+ 1)

Here it is clear that output voltage is approximately equal to logarithm of the input supply. However

some limitations of this circuit are

3. Its response is very temperature sensitive (note the T and Io terms in the transfer equation).

4. Diodes do not provide a good log conformity, which means that the relationship between their

forward voltage and their current does not accurately follow a logarithmic form.

To overcome these limitations transdiode has been used in this project. Transistors provide a far better

conformity than diodes. The bipolar transistor offers this best performance due to the fact that its

conduction is based upon majority carrier, either electrons or holes, whereas diode conducts with both

electrons and holes. The transdiode configuration of the BJT is as shown in figure 3.3.

Fig. 3.3 Transdiode configuration of BJT for log converter

The diode connected transistor has following salient point:

3.4

3.5

18

The logging range is limited to 4 or 5 decades of input voltage since the base current is added

to the collector current of the transistor.

It usually has a faster, stable dynamic response.

Polarity of the circuit can be easily changed by reversing the transistor.

Using a transistor with a high β (hFE) for good log conformity.

From the circuit of Fig. 3.3, we evolve to the more practical circuit of Fig. 3.4. The capacitor across

the npn transistor is used to reduce the ac gain while the diode protects the transistor against excessive

reverse base-to-emitter voltage.

Fig 3.4 Log Converter circuit implemented

3.2.2 Anti-Log Converters:

The basic circuit is very similar to the elementary log converter except that the diode and the resistor

are swopped around. The antilog function is achieved using the voltage and current log relationship of

the p-n junction as described previously for the log converter.

Iin = Io( 𝑒4∙𝑉𝑖𝑛

𝑘𝑇 − 1)

Vout = -I0RF( 𝑒4∙𝑉𝑖𝑛

𝑘𝑇 − 1) = IoRF( 𝑒4∙𝑉𝑖𝑛

𝑘𝑇 )

The antilog converter circuit used is as shown in fig 3.5

Fig. 3.5 Antilog converter

Using both the logarithmic and antilogarithmic amplifier circuits, we can either multiply or divide

input voltages. The two basic relationships of logarithms are:

3.6

3.7

19

log (AB) = log A + log B

log (A/B) = log A - log B

By summing the logarithms of two input voltages A and B, and using the antilog circuit, we can then

obtain the product of A and B, as shown in Fig. 3.6.

Fig. 3.6 Multiplication of two input signals using log and antilog amplifier

3.3 First order low pass Filter

A first order low pass filter uses a RC network for filtering. A simple RC works as a low pass filter

with the input applied across both R and C in series while output is taken across C element. The circuit

diagram of the low pass filter is shown in fig 3.7.

Fig: 3.7 Circuit diagram of a Low pass filter

Suppose the voltage across the capacitor is Vc (t). In this case, the output voltage is related to the input

voltage through the linear constant- coefficient differential equation

RC 𝑑𝑉𝑐

𝑑𝑡 + Vc(t) = V(t)

The system determined by the above equation is LTI. In order to determine its frequency response we

have the following derivation:

Input voltage V(t) = 𝑒𝑗𝜔𝑡

Output voltage Vc(t) = H(j𝜔)𝑒𝑗𝜔𝑡

Substituting the above expressions in the differential equation, we get

RC 𝑑[𝐻 𝑗𝜔 𝑒 𝑗𝜔𝑡 ]

𝑑𝑡 + H(j𝜔)𝑒𝑗𝜔𝑡= 𝑒𝑗𝜔𝑡

R1

C1V

3.8

3.9

3.10

3.11

3.12

3.13

20

j𝜔RC H(j𝜔)𝑒𝑗𝜔𝑡 + H j𝜔 𝑒 𝑡 = 𝑒𝑗𝜔𝑡

Thus the equation becomes as

H(j𝜔) 𝑒𝑗𝜔𝑡 = 𝑒 𝑗𝜔𝑡

1+RCj 𝜔

H j𝜔 = 1

1+RCj 𝜔

This is the Transfer function of the above circuit diagram.

Here we see that for frequencies near=0, |H j𝜔 | is nearly equal to 1. While for larger values of

frequencies the magnitude is considerably small and steadily decreases as frequency increases. The

Frequency Response of a specified Transfer function is as shown in fig 3.8

Fig 3.8 Frequency plot with RC=0.0001

Here we can see that the magnitude gain decreases as frequency goes past the cut off frequency of the

filter.

3.4 Result

Misers output as the difference in frequencies of two signals was obtained. We have mounted our

circuit on PCB whose image is shown in fig 3.9

Pin configuration in the figure is as follows:

1. +15 volt (positive supply for op-amp)

2. Blank for future use

3. 15 volt (negative supply for op-amp)

3.14

3.15

3.16

21

4. Ground

5. First input signal

6. Ground

7. Output signal as the difference of frequencies of input signals

8. Second input signal

Our observed output waveform was as seem below-

Fig 3.9 PCB layout of the designed Mixer

The observed outputs were as shown in fig3.10

Fig 3.10 Mixer Output as observed on DSO

5

6

7

8

1 2 3 4

22

CHAPTER 4

ANALYSIS AND DISCUSSION

23

4.1 Overall Analysis of Mixer

Telecommunication as we say is the future of mankind, without it the life of a modern day man would

not have been possible. It is not only limited to personal use of a person. It is also an important to a

national defence to have a strong and rigid system so that it can be used effectively as and when

needed. The modern day devices Mobiles, Radars etc are a reflection of the level to which the

telecommunication has crept into our life and so has lead to the rise in the need of better

communication systems. Frequency mixers are a very essential component used in telecommunication

systems and thus form a very bright future prospect. People have been constantly working on

improving the performance of the designs that have been proposed in this field till date.

Frequency mixers are basically used to translate the frequency from a higher value to a lower value,

which is usually required in case of RF frequencies which have the case of design constraints when it

comes to the design of amplifiers or other systems at that frequencies, one of them is a low value of

gain that can be provided at these frequencies. Thus to process a given signal it is first translated to a

lower frequency value, processed and then again translated upwards.

Mixers find use in a variety of applications. It is used to translate microwave frequencies that are a

very important application in Telecom. Furthermore, they are used in Radios which can be frequency

modulated or amplitude modulated where the signal is translated to a specified frequency which is the

same frequency used world over. It is a basic entity of almost every telecommunication system. It is

also used by Radar systems, television and Amplitude and frequency modulation based stations to

generate the modulated wave. In any case a translation of the frequency is needed; mixer is the best

remedy available. Thus Frequency mixer has been an important topic of research for people and a

variety of mixers have been designed and implemented industrially as well as on project level. We can

say that mixer will have its relevance till the modern day man has its dependence on

telecommunication and communications systems and the fight to achieve the best at the earliest will go

on.

In our project we have implemented a LAB design of Frequency mixer which takes 2 input signals and

mixes them using the concept of log amplification followed by addition and then the antilog

amplification which generate the product of the 2 input signals. The Modulation products are a mixture

of frequency components which can be separated with the use of an appropriate filter; we have used a

low pass filter which filters out the down translated frequency component.

As we know that mixers are an important class of circuits used in many wireless and microwave

applications. In principle it produces the sum and the difference of the 2 input frequencies, however in

reality the output also contains various intermodulation products, resulting from the non linear

24

behaviour of the Mixer. Diversion from the ideal multiplication introduces undesired intermodulation

products which in some cases are difficult of even impossible to reject because they appear in the pass

band of the filter. Also the use of analog circuit limits the integraibility of this circuit with the digital

circuits. Thus the design of the filter becomes an important aspect of mixer design as the purpose of

the design is not served if the correct modulation products are not obtained using the defined analog

circuitry. One of the Major problems that occur with the filter design is the limited dynamic range. The

distortion in the active devices leads to a maximum signal less than or equal to the supply voltage. The

noise produced by the active/passive conductance’s in the filter circuit leads to a minimum value of the

signal that can be processed. In many cases the low dynamic range of the filter leads to limited

performance of the system which thus limits the use of that system. In our design we have used the

transistor a diode, but here MOSFETS can be used in place of it.

Mixers are basically made up from Analog multipliers and multipliers form an integral part of many

electronic systems. The offset in the multiplier can decrease the multiplier’s gain, degrade its noise

performance and minimum detectable signal and increase the non linearity and distortion produced by

the multiplier in the modulation process. Thus we need a mechanism to compensate for the errors

caused by these problems. In addition to a filter a radio receiver also uses a device called diplexer

which absorbs undesired mixer outputs so that they are not reflected back into the mixer, if the mixer

circuit is not properly terminated by proper load impedance.

There are several non-idealities in mixers that need to be considered in design. Noise, linearity,

dynamic range and isolation are discussed briefly. Noise figure characterizes how effective the device

is at rejecting noise while maintaining the signal. It is defined as the ratio of input signal-to-noise

ratio (SNR) to output IF SNR. It varies across different types of mixers because it is highly dependent

on whether or not both output frequencies are desired. If both bands (frequencies) are desirable

because they contain useful information, there is twice the signal power. Noise figure improves in

this case, which is termed the double-sideband (DSB) case. In the single-sideband (SSB) case

where only one of the bands is considered, the noise figure is degraded by 3 dB (3dB = 10

log(0.5)). In the case that the mixer has the worst noise figure in the system additional pre-

mixer stages may be necessary to improve the noise figure of the system. If SSB is preferred,

it is possible that an image rejection filter will be implemented before the mixer to greatly

attenuate the image signal before mixing. Here, linearity and dynamic range are also important in

mixer design. Linearity characterizes how the mixer output amplitude (power) varies as the input

amplitude (power) changes, at a given frequency. Besides noise figure, gain, and power

considerations, the mixer must maintain linear operation with both strong and weak input signals.

Distortion, in particular when a weak signal is in presence of a strong interfering signal, must

be minimized. This is crucial in the application of ultrasound. Dynamic performance of the system

25

may be dominated by the dynamic performance of the mixer as it is not only the first element in

the signal chain but also a challenging element to design.

4.2 Existing Problems

Thus there are several problems in the existing mixer design which can be worked upon and are

discusses under the following headings:

4.2.1 Using rectifiers in place of DC offset

The main problem due to which DC offset has been provided is that while taking logarithm of input

signal our input signal should always be greater than zero in order to have proper output. Alternative

solution is to use rectifier circuit with the input signals in order to make effective input signal of the

op-amp always greater than zero. Two types of rectifier circuits can be used-

1. Using Half wave rectifier

We can provide a half wave rectifier at the input signal in order to get proper logarithm of input

signals. A half wave circuit can be easily made by using a diode-

Fig 4.1 Half wave Rectifier

But the main problem that would be associated with this circuit would be that our message

signal would be lost during negative half cycle. To avoid this we may use an full wave rectifier

circuit.

2. Using full wave rectifiers- In order to get proper effective input voltage as well as avoiding the

loss of message signal we can use a full wave rectifier. A full wave rectifier circuit can be

easily made using a diode bridge-

Fig 4.2 Full Wave Rectifier

26

This circuit can easily rectify the input voltage but again there would be a problem. The new

problem would be that our both the input frequencies would be double and thus the result

which should be come as output would also be doubled.

A possible solution would be that we use a zero crossing detector circuit of the rectified wave

and design a circuit such that it would invert the output pulse at every alternate zero detection.

This may be suitable best design.

4.2.2 Better filter design: When dealing with filter circuits, it is always important to note that the

response of the filter depends on the filter's component values and the impedance of the load. If a cut-

off frequency equation fails to give consideration to load impedance, it assumes no load and will fail to

give accurate results for a real-life filter conducting power to a load. The cut off frequency needs to be

calculated carefully according to the desired application. The above project uses a Low pass filter

which is a 1st order Butterworth (a filter is a Butterworth filter which has a flat response from its zero

frequency to its cut-off frequency) whose response is not really close to the response of an ideal filter.

Although it attenuates the frequencies higher than the cut off frequency but the filter output still consist

of this frequency which leads to a problem when only some specific frequencies are desired in the

output. Thus a better response of the low pass filter without increasing its order can be worked out to

improve the credibility of the mixer.

4.2.3 Chopper stabilization: With chopper stabilization, a technique long used to achieve low-

offset amplification, can be applied to multipliers to continuously reject DC offset without sacrificing

DC performance. Chopping has been applied to specific types of multipliers before for various

applications. In prototype multiplier chopping is used to reduce the second-order intermodulation

distortion and noise of a down-conversion mixer. A similar technique is used to reduce the

temperature-dependent offset of a squaring circuit used for power measurement. Chopping is also

applied in to reduce the offset of the demodulator (that is mixer) in a temperature-to-frequency

converter. Thus in order to improve the overall performance of the filters it is important to have a

improved design of the multiplier(Logarithmic and Antilogarithmic circuit in the project) which

makes chopper design another aspect which can be worked upon.

4.2.4 Diplexer design: The Mixers are basically used at RF frequencies. The RF mixer is basically

like a RF circuit and like any other RF circuit it wants to be terminated by characteristic impedance

otherwise a standing wave exists in the circuit which causes signal loss and many other problems. A

Diplexer does 2 jobs, firstly it removes or absorbs the undesired mixer output signals so that they are

not reflected back into the mixer and secondly it transmits the rest of the signals through to the output.

A simple diplexer circuit consists of a series and parallel tank circuits. Although various kinds of

27

diplexers are available with mixers, it is yet another improvement which can be made to the present

design to improve the mixing characteristics.

The mathematical derivations of the circuit implemented shows that the temperature sensitivity of the

design is very poor, resulting in temperature dependent errors. The system bandwidth is narrower for

small signals as the emitter resistance is high for small values of currents. Also the source impedance

of the input signals applied to the input should be smaller as compared to the input resistance then only

the logarithmic amplifier works efficiently.

Using a p-n-p transistor in the above design limits the logarithmic range which leads to degradation of

the performance in comparison to using the n-p-n transistors. The circuit implemented above also

needs the following modifications to give better results:

Provision of base-emitter junction protection.

Reduction of temperature effects.

Consideration of bulk resistance errors.

Consideration of Op-Amp offset errors.

Provision of giving bipolar signals as input.

Improvement of frequency stability of the system.

Although negative signals can be applied to the logarithmic amplifier by using a precision rectifier but

this method also fails as it adds errors from the rectifier.

4.3 Discussions

4.3.1 Providing dc offset to input signals:

Consider the two input signals-

𝑣1 = 𝐴1 cos 2𝜋𝑓1𝑡

𝑣2 = 𝐴2cos(2𝜋𝑓2𝑡)

The value of first input signal varies from +A1 to –A1 and from value of second input signal varies

from –A2 to +A2. If we do not apply offset at input terminals then when we try to take logarithm of

input signals then it becomes impossible because logarithmic of input signals are not defined. In order

to avoid this problem if we apply offset voltage of +A1 and +A2 to both of the input signals

respectively then also we may not get satisfactory output since logarithmic of any number smaller than

1 is negative and for values nearer to zero it goes up to -∞.

4.1

4.2

28

So in this case also it will lead to the negative saturation of op-amp and leading the information to lose.

Fig 4.3 Plot showing effect of no-offset

But if we apply input offset voltage of +A1+1 for the first input signal and of +A2+1 for the second

signal then ours input voltage will be grater then 1 in every condition and we will get an satisfactory

output.

Fig 4.4 Plot showing effect of offset

29

4.3.2 Avoiding subtraction of Spur terms

Now consider the modified input signals as

𝑉1 = 𝑣1 + 𝐷1

𝑉2 = 𝑣2 + 𝐷2

Now if we multiply these signals

𝑉0 = 𝑉1 ∗ 𝑉2

𝑉0 = 𝑉1 ∗ 𝑉2 + 𝑉1 ∗ 𝐷2 + 𝑉2 ∗ 𝐷1 + 𝐷1 ∗ 𝐷2

Since offset D1 and D2 has been provided by us so we know its value. It seems from these equations

that if we subtract spur terns D1V1 and D2V2from the output then we will get remaining signal

consisting of V1V2 terms only (there would be a dc voltage term also but it is not matter of worry). But

this process may not be so simple. Since when we take the logarithm of the input signal then output of

logarithm is not exactly equal to the input signals but it is proportional to input signals. Coefficient of

proportionality is not always equal to one but it is dependent upon parameters of components (like-

diode, capacitor, transistor) used. So we cannot always say that coefficient of equal to 1.

So we can conclude here that subtraction of spur terms may not lead to remove these terms completely

been removed from output and same had been proved experimentally these even by using subtraction

circuit in the end we are not able to remove hose terms.

4.3.3 Low pass filter: Since there are terms of many harmonics at the output so we can observe

directly the output waveforms on DSO. So in order to view output waveforms we have to put an low

pass filter at the output which will attenuate the higher frequency terms and remaining term will

consist the frequency terms equal to subtraction of both the input frequencies. Here we are providing at

low pass filter at the cutoff frequency of 5KHz which is standard cutoff frequency of message signals.

Thus overall, we can say , MIXER designing itself has lot of opportunities to work upon and better we

design the mixer, better it will prove for our communication technology.

4.3

4.4

4.5

4.6

30

References :

[1] A. J. Peyton, V. Walsh, ―Analog electronics with Op Amps: a source book of practical

circuits‖, Cambridge University Press, pp 160-200,

[2] Adel S. Sedra, Kenneth C. Smith and Arun N. Chandorkar, ―Micro Electronics Circuits

Theory and Applications‖, Oxford University, Vol 5th

, no 4, pp 999-1037, 2010.

[3] [4] Jacob Milliam and Christos C. Halkias, ― Integrated Electronics‖, Mcgraw Hill, Vol

47th

,pp 501-510,2008.

[4]. 1993Ramakant A. Gayakwad, ―Op-Amps and Linear Integrated Circuits‖, Pearson

Education, vol 4th

, pp 303-320, 2008.

[5] Jacob Milliman and Arvin Grabel, ―Microelectronics and integrated circuits‖, Mcgraw Hill,

Vol 2nd

, no 3, pp 367-385, 2006.