analog communications lab

Analog Communications Lab

INDEX

S.No Name of the ExperimentPage

No

Date of

Performance

Date Of

Submission

Assessment

of marks

(Max 10M)

Sign. Of

Faculty

1.Amplitude Modulation &

Demodulation

2. Diode Detector Characteristics

3.Frequency Modulation &

Demodulation

4. Balanced Modulator

5. Pre-Emphasis & De-emphasis

6. Mixer Characteristics

7. Digital Phase Detector

8. Phase Locked Loop

9. Synchronous Detector

10 AGC Characteristics

11 Frequency Synthesizer

12. Squelch Circuit

Average marks

Signature of Lab-In-charge HOD

Turbomachinery Institute Science & Technology 1 Dept. of ECE


INSTRUCTIONS TO STUDENTS

Students shall read the points given below for understanding the theoretical concepts and Practical applications.

1. Listen carefully to the lecture given by teacher about importance of subject, curriculum philosophy, Learning

structure, skills to be developed, information about equipment, instruments, procedure, method of continuous

assessment, tentative plan of work in Laboratory and total amount of work to be done in a semester.

2. Students shall undergo study visit of the laboratory for types of equipment, instruments and material to be

used, before performing experiments.

3. Read the write up of each experiment to be performed, a day in advance.

4. Organize the work in the group and make a record of all observations.

5. Understand the purpose of experiment and its practical implications.

6. Student should not hesitate to ask any difficulty faced during conduct of practical / exercise.

7. Student shall develop maintenance skills as expected by the industries.

8. Student should develop the habit of pocket discussion / group discussion related to the experiments/

exercises so that exchanges of knowledge / skills could take place.

9. Student should develop habit to submit the practical, exercise continuously and progressively on the

scheduled dates and should get the assessment done.

10. Student shall attempt to develop related hands - on - skills and gain confidence.

11. Student shall focus on development of skills rather than theoretical or codified knowledge.

12. Student shall visit the nearby workshops, workstation, industries, laboratories, technical exhibitions trade fair

etc. even not included in the Lab Manual. In short, students should have exposure to the area of work right in the

student hood.

13. Student shall develop the habit of evolving more ideas, innovations, skills etc. those included in the scope of

the manual.

14. Student shall refer to technical magazines, proceedings of the Seminars, refer websites related to the scope

of the subjects and update their knowledge and skills.

15. The student shall study all the questions given in the laboratory manual and practice to write the answers to

these questions.



Exp No: 1 Date:

AMPLITUDE MODULATION & DEMODULATION

AIM: To study the function of Amplitude Modulation & Demodulation (under modulation, perfect

modulation & over modulation) and also to calculate the modulation index.

APPARATUS REQUIRED:

S. No. Component Specification Quantity

1 Transistor BC107 2

2 Resistors

100KΩ 2

4.7KΩ 2

270 Ω 1

33 Ω 1

3 Capacitors4.7µF 2

0.001µF 1

4 Diode 0A79 1

5 Functions Generator 1Mhz 2

6 Regulated Power Supply (0-30)V 1

7 Bread Board 1

8 Cathode Ray Oscilloscope 0-20MHz 1

9 Connecting Wires Single Strand As Required

THEORY:

Modulator section illustrates the circuit of modulating amplifier employing a transistor as an active device in

CE mode. R1 & R2 establish a quiescent forward bias for the transistor. The modulating signal fed at the

emitter section causes the bias to increase or decrease in accordance with the modulating signal. C 3 is bypass

capacitor for carrier. Thus the carrier signal applied at the base gets amplified more when the amplitude of

the modulating signal is at its maximum and less when the amplitude of the modulating signal is small. C 2

couples the modulated signal to output of the modulator. Demodulation involves two operations.

i) Rectification of the modulated signal and

ii) Elimination of RF components of the rectified signal.

The diode in the circuit diagram of demodulator does half wave rectification. The rectified signal is applied

to a low pass filter to extract the modulating signal.



CIRCUIT DIAGRAM:

VCC = 12V

R1 R3

C2

Output

C1 B C L1 100H

RF Input BC 107

R2 E

R4 C3

AF Input

Demodulator:

D1

AM Input AF Output

OA 79 1K

EXPECTED WAVEFORMS:-



PROCEDURE:

1. Made the connections according to Circuit Diagram.

2. Measure and note down the frequency & amplitude (p-p) of the fixed carrier signal.

3. Measure and note down the frequency & amplitude (p-p) of the fixed message signal.

4. Apply fixed frequency carrier signal to RF input terminals.

5. Apply modulating signal to AF input terminals.

6. Note down and trace the modulated signal envelope on the CRO screen.

7. Find the modulation index by measuring Vmax and Vmin from the modulated (detected/ traced)

envelope.

m=(Vmax –Vmin)/(Vmax+Vmin)

8. Repeat the steps 4,5 & 6 by changing the amplitude of the modulating signal so as to observe over

modulation, under modulating and perfect modulation.

9. For demodulation, apply the amplitude modulated signal as an input to the demodulator and

verify the demodulated output with respect to the applied modulating signal

PRECAUTIONS:

RESULT:



QUESTIONS

1. AM is Defined as ____________

2. Draw its spectrum___________

3. Draw the phase representation of an amplitude modulated wave___

4. Modulation index is defined as_____

5. The different degrees of modulation _______

6. What are the limitations of square law modulator

7. Compare linear and nonlinear modulators

8. Compare base modulation and emitter modulation

9. AM Demodulator is ___________

10. Detection process _________

11. The different types of distortions that occur in an envelop detector are__________

12. Elimination of distortions in Envelope Detector __________________ technique we use.


Tm


Exp No: 2 Date:

DIODE DETECTOR CHARACTERISTICS

AIM: To perform demodulation of an amplitude modulated signal using

(i) Simple diode detector and (ii) Practical diode detector

APPARATUS REQUIRED:


1 Transistor BC107 2

2 Resistors

100KΩ 2

4.7KΩ 2

270 Ω 1

33 Ω 1

3 Capacitors

4.7µF 2

0.001µF 1

Variable 2

4 Diode 0A79 1



7 Bread Board 1


9 Potentiometer 100K Ω 1


THEORY: Demodulation involves two operations:

(i) Rectification of the modulated wave and

(ii) Elimination of RF components of the rectified modulated wave

Simple Diode Detector

The diode is the most common device used in AM demodulator. Signal (AM modulated signal) is

applied to anode and output is taken from cathode. Diode operates as half wave rectifier and passes only

positive half cycle of the modulated wav e. Further signal is applied to a parallel combination of resistor (Rd)

and capacitor (Cd) which acts as a low pass filter. This LPF allows only low frequency signal to output and it

by passes RF component to the ground.

This simple diode detector has the disadvantage that the output voltage, in addition to being

proportional to the modulating signal, also has a dc component, which represents the average envelope

amplitude (i.e. carrier signal) and a small RF ripple. However these unwanted components are removed in a

practical detector leaving only AF signal.



CIRCUIT DIAGRAM:

EXPECTED WAVEFORMS:-

AM Modulated signal



Practical Diode Detector:

In practical diode detector the cathode terminal of the diode is connected to one end of the secondary

of IF transformer. The other end is grounded. Secondary is tuned with the capacitor C1. The capacitors C2

and C3 are used for RF filtering.

The modulated signal is applied at the input of IF transformer. The voltage applied is negative and

hence the cathode of the diode passes is connected to the IF transformer. So the diode passes both the

positive and negative half cycles. The RF filtering is done by C2 and C3. The output is taken at the volume

control.

PROCEDURE:-

1. Connect the circuit as per the circuit diagram and switch on the power supply. ( Measure the

power supply voltage, +12V and -12V)

2. Observe outputs of RF and AF signal generator using CRO, note that RF voltage is

approximately 300mv p-p of 1MHz frequency and AF voltage is 10V p-p 2KHz frequency.

3. Now connect the modulator output to the simple diode detector input.

4. Observe the AF signal at the output to the simple diode detector at approximately 50%

modulation using CRO.

5. Compare it with the original AF and observe that the detected signal is same as the AF signal

applied. Thus no information is lost in the process of modulation. (Note: Only wave shape and

frequency will be same, amplitude will be attenuated and phase may change)

6. To observe AM wave at different frequencies, connect AF signal from external signal generator to

the input of modulator and observe demodulated wave at different frequencies.

7. Repeat the experiment using practical diode detector circuit.

PRECAUTIONS:

RESULT:



AF output



QUESTIONS

1. Selectivity of receiver is defined as _____________

2. Sensitivity of a receiver is defined as ____________

2. The purpose of diode in diode detector circuit is __________

3. The disadvantages of simple diode detector circuit are _______

4. The factors influencing the choice of intermediate frequency in receivers _____

5. The advantages of practical diode detector are________


Tm


Exp No: 3 Date:

FREQUENCY MODULATION AND DEMODULATION

AIM: To study the functioning of frequency modulation & demodulation and to calculate the modulation

index.

APPARATUS REQUIRED


1 ICs XR 2206, LM 565 1 Each

2 Resistors

100KΩ, 4.7KΩ 2 Each

10KΩ 1

220Ω 1

47KΩ 1

3 Capacitors

0.01µF,0.001µF 2

0. 1µF, 470pF, 0.01pF 1

1µF,10µF 1



6 Bread Board 1



THEORY:

1. AF Generator:

This is an op-amp placed wein bridge oscillator. A FET input quad Op-Amp (ICTL084) is used here

to generate low frequency signals of 500 Hz and 5KHz to use as modulating signal. In this

experiment, a switch is provided to change the frequency. Required amplification is provided to

avoid loading effect.

2. Regulated power supply:

This consists of bridge rectifier, capacitor filters and three terminal regulators to provide required dc

voltages in the circuit i.e. +15 V, -15 V, +5V .

3. Modulator:

This has been developed using XR-2206 integrated circuit. The IC XR-2206 is a monolithic Function

generator; the output waveforms can be both amplitude and frequency modulated by an external

voltage. Frequency of operation can be selected externally over a range of 0.01 MHz. The circuit is

ideally suited for communications, instrumentations and function generator applications requiring



CIRCUIT DIAGRAM:

Frequency Modulation Circuit Diagram:

+12v 4.7K

4.7 10F/63v 100K 47K K

AF I/F FM O/P

10K 0.1F

2200.01F

1F/63v

Frequency Demodulation Circuit Diagram:+ 5v

10K 10KPF

0.1FAF Input

680 1KPF

AF Output

680 470PF

– 5V


4

7 3

2

XR 2206

14

5

6 13

1 10

10

2

8

LM 565

7

4

3 5

1 9


sinusoidal tone, AM, FM or FSK generation. In this experiment, IC XC-2206 is connected to

generate sine wave, which is used as a carrier signal. The amplitude of carrier signal is 5vPP of 100

KHz frequencies.

4. Demodulator:

This had been developed using LM4565 integrated circuit. The IC LM565 is a general-

purpose phase locked loop containing a stable, highly linear voltage controlled oscillator for low

distortion FM demodulation.

The VCO free running frequency f0 is adjusted to the center frequency of input frequency

modulated signal i.e. carrier frequency which is of 100 KHz. When FM signal is connected to the

demodulator input, the deviation in the input signal (FM signal) frequency which creates a DC error

voltage at output of the phase comparator which is proportional to the change of frequency f. This

error voltage pulls the VCO to the new point. This error voltage will be the demodulated version of

the frequency modulated input signal.

PROCEDURE:

1. Connect the circuit as per the given circuit diagram.

2. Switch on the power supply.

3. Measure the frequency of the carrier signal at the FM output terminal with input terminals open and plot

the same on graph.

4. Apply the modulating signal of 500HZ with 1Vp-p.

5. Trace the modulated wave on the C.R.O & plot the same on graph.

6. Find the modulation index by measuring minimum and maximum frequency deviations from the carrier

frequency using the CRO.

7. Repeat the steps 5& 6 by changing the amplitude and /or frequency of the modulating Signal.

8. For demodulation apply the modulated signal as an input to demodulator circuit and compare the

demodulated signal with the input modulating signal & also draw the same on the graph.

NOTE: Note down all the input and output wave forms of the signals applied and obtained respectively.

PRECAUTIONS:

RESULT:



EXPECTED WAVEFORMS:



QUESTIONS

1. Frequency modulation is defined as ____

2. The advantages of indirect method of FM generation are __

3. Modulation index and frequency deviation of FM is ____

4. The advantages of FM are ______

5. Narrow band FM is _____

6. Compare narrow band FM and wide band FM?

7. Differentiate FM and AM _____

8. FM wave can be converted into PM wave _____

9, State the principle of reactance tube modulator _____

10. The bandwidth of FM system is ___

11. The function of FM discriminator is_________

12. Ratio detector differ from foster-seely discriminator _____

13. Linear detector is ________

14. The drawbacks of slope detector are ___________



Ex



p No: 4 Date:

BALANCED MODULATOR

AIM: To study the following of the Balanced Modulator as a

1. Frequency Doubler

2. DSB-SC Generator.

APPARATUS REQUUIRED:


1 Modulator IC MC1496 2

2 Resistors

10KΩ 3

4.7KΩ 2

270 Ω 1

33 Ω 1


0.001µF 1



7 Bread Board 1



THEORY:

1. RF Generator:

Colpitts oscillator using FET is used here to generate RF signal of approximately 100 KHz Frequency to use

as carrier signal in this experiment. Adjustments for Amplitude and Frequency are provided in panel for ease

of operation.

2. AF Generator:

Low Frequency signal of approximately 5KHz is generated using OP-AMP based Wein- Bridge oscillator.

IC TL 084 is used as an active component; TL 084 is FET input general purpose quad OP-AMP integrated

circuit. One of the OP-AMP has been used as amplifier to improve signal level. Facility is provided to

change output voltage.

3. Regulated Power Supply:

This consists of bridge rectifier, capacitor filters and three terminal regulators to provide required DC

voltage in the circuit i.e. +12v, -8v @ 150 MA each.



CIRCUIT DIAGRAM:



4. Modulator:

The IC MC 1496 is used as Modulator in this experiment. MC 1496 is a monolithic integrated circuit

balanced modulator/Demodulator, is versatile and can be used up to 200 Mhz. Multiplier: A balanced

modulator is essentially a multiplier. The output of the MC 1496 balanced modulator is proportional to the

product of the two input signals. If you apply the same sinusoidal signal to both inputs of a ballooned

modulator, the output will be the square of the input signal AM-DSB/SC: If you use two sinusoidal signals

with deferent frequencies at the two inputs of a balanced modulator (multiplier) you can produce AMDSB/

SC modulation. This is generally accomplished using a high- frequency “carrier” sinusoid and a lower

frequency “modulation” waveform (such as an audio signal from microphone). The figure 1.1 is a plot of a

DSB-SC waveform, this figure is the graph of a 100KHz and a 5 KHz sinusoid multiplied together. Figure

1.2 shows the circuit that you will use for this experiment using MC 1496 balanced modulator/demodulator.

Note: In frequency doubling If the input time period is “T” after frequency doubling the time period should

be halfed.i.e,”T/2”.

PROCEDURE:-

I-Frequency Doubler

1. Connect the circuit as per the given circuit diagram.

2. Switch on the power to the trainer kit.

3. Apply a 5 KHz signal to both RF and AF inputs of 0.1VP-P.

4. Measure the output signal frequency and amplitude by connecting the output to CRO.

5. Repeat the steps 3 and 4 by changing the applied input signal frequency to 100KHZ and 500KHz.

And note down the output signals.

NOTE: - Amplitude decreases with increase in the applied input frequency.

II-Generation of DSB-SC

1. For the same circuit apply the modulating signal(AF) frequency in between 1Khz to 5Khz having 0.4

VP-P and a carrier signal(RF) of 100KHz having a 0.1 VP-P .

2. Adjust the RF carrier null potentiometer to observe a DSB-SC waveform at the output terminal on

CRO and plot the same. Repeat the above process by varying the amplitude and frequency of AF but

RF maintained constant.

NOTE:- Note down all the waveforms for the applied inputs and their respective outputs.

PRECAUTIONS:



EXPECTED WAVEFORMS:

RESULT:



QUESTIONS

1. The two ways of generating DSB_SC are ________

2. The applications of balanced modulator are ________

3. The advantages of suppressing the carrier ________

4. The advantages of balanced modulator __________

5. The advantages of Ring modulator __________

6. The expression for the output voltage of a balanced modulator is _________



Exp No: 5 Date:

PRE-EMPHASIS & DE-EMPHASIS

AIM: To study the functioning of Pre-Emphasis and De-Emphasis circuits.

APPARATUS REQUIRED:


1 Resistors 1KΩ 2


0.001µF 1



5 Bread Board 1



THEORY:

Frequency modulation is much immune to noise than amplitude modulation and significantly more

immune than phase modulation. A single noise frequency will affect the output of the receiver only if it falls

with in its pass band.

The noise has a greater effect on the higher modulating frequencies than on lower ones. Thus, if the

higher frequencies were artificially boosted at the transmitter and correspondingly cut at the receiver,

improvement in noise immunity could be expected. This booting of the higher frequencies, in accordance

with a pre-arranged curve, is termed pre-emphasis, and the compensation at the receiver is called de-

emphasis. If the two modulating signals have the same initial amplitude, and one of them is pre-emphasized

to (say) twice this amplitude, whereas the other is unaffected (being at a much lower frequency) then the

receiver will naturally have to de-emphasize the first signal by a factor of 2, to ensure that both signals have

the same amplitude in the output of the receiver. Before demodulation, i.e. while susceptible to noise

interference the emphasized signal had twice the deviation it would have had without pre-emphasis, and was

thus more immune to noise. Alternatively, it is seen that when this signal is de-emphasized any noise

sideband voltages are de-emphasized with it, and therefore have a correspondingly lower amplitude than

they would have had without emphasis again their effect on the output is reduced. The amount of pre-

emphasis in U.S FM broadcasting, and in the sound transmissions accompanying television, has been

standardized at 75 microseconds, whereas a number of other services, notably CCIR and Australian TV

sound transmission, use 50 micro second.

CIRCUIT DIAGRAM:



The usage of microseconds for defining emphasis is standard. 75 microseconds de-emphasis corresponds to

a frequency response curve that is 3 db down at the frequency whose time constant is RC is 75

microseconds. This frequency is given by f=1/2ÐRC and it is therefore 2120 Hz; with 50-microseconds de-

emphasis it would have been 3180 Hz. Figure I shows pre emphasis and de-emphasis curves for a 7

microseconds emphasis, as used in the united states. If emphasis is applied to amplitude modulation, some

improvement will also result, but it is not as great as in FM because the highest modulating frequencies in

AM are no more affected by noise than any others.

Apart from that, it would be difficult to introduce pre-emphasis and de-emphasis in existing AM

services since extensive modifications would be needed, particularly in view of the huge numbers is

receivers in use.

PROCEDURE:

I-PRE-EMPHASIS

1. Connect the circuit as per the circuit diagram

2. Apply a sine wave to the input terminals of 2 VP-P (Vi)

3. By varying the input frequency with fixed amplitude, note down the output amplitude (Vo) with

respect to the input frequency.

4. Calculate the gain using the formula

Gain = 20 log (VO/ VI) db

Where VO = output voltage in volts.

VI = Input voltage in volts.

And plot the frequency response.

II-DE-EMPHASIS

1. Connect the circuit as per circuit diagram.

Repeat steps 2, 3 & 4 of Pre-Emphasis to de-emphasis also.

PRECAUTIONS:

RESULT:



QUESTIONS

1. The need for pre-emphasis __________

2. The operation of pre-emphasis circuit __________

3. Pre-emphasis operation is similar to high pass filter explain how_______

4. De-emphasis operation is similar to low pass filter justify _______

5. De-emphasis is _______

6. Draw the frequency response of a pre-emphasis circuit_______

7. Draw the frequency response of a de-emphasis circuit ______

8. Give the formula for the cutoff frequency of the pre-emphasis circuit ______

9. The significance of the 3db down frequency is ______



Exp No: 6 Date:

CHARACTERISTICS OF MIXER

AIM: To study the functioning of a frequency mixer.

APPARATUS REQUIRED:


1 Resistors

4.7KΩ, 22KΩ,3.3KΩ 1

27KΩ, 6.2KΩ 3

10KΩ 3

2 Capacitors

0.1µF, 50pF 2

0.1µF 2

100pF 4

3 Transistor BC 547 1



6 Bread Board 1



THEORY:The fundamental principle of modulation involves the mixing or multiplying of a low frequency

signal with a higher frequency signal such as an AM or FM carrier. This enables the information contained

in the low frequency signal to be transmitted through space as high frequency electromagnetic waves.

Commercial radios use as intermediate frequency (455 khz for commercial AM). These if carrier contain all

the information available to the receiver but in order to obtain this information mixing must take place to

obtain the lower frequency signals ‘riding’ onto IF or RF frequency. This principle is also used in mixing

low frequency signals up to IF or RF frequencies. The purpose of this experiment is to observe the effect of

mixing two frequencies using a nonlinear single transistor mixer and to demonstrate the use of a band stop

and a 2-pole low pass filter in a practical application.

BLOCK DIAGRAM DESCRIPTION:

1. RF Generator 1:

Colpitts oscillator using FET is used here to generate RF signal of approximately 500 KHz to

use as local oscillator in this experiment. Adjustments for amplitude and Frequency are

provided on panel for ease of operation.



CIRCUIT DIAGRAM:

12V

50pF 50pF

3.3K 22K 4.7K

27K 6.2K 6.2K 27K Output C 0.1F B BC 547 100pF 100pF 100pFVX

E 0.1F

VY 10K 10K

10K

EXPECTED WAVEFORMS:



2. RF Generator 2:

Colpitts oscillator using FET is used here to generate RF signal of approximately 520 KHz to

use as IF Signal in this experiment. Adjustment for Frequency is provided on panel to get

exact frequency.

3. Regulated Power Supply:

This consists of bridge rectifier, capacitor filters and three terminal regulators to provide

required do voltage in the circuit i.e., +12v @150 mA.

4. Mixer:

Mixing is the nonlinear combination of two signals to produce sum and difference frequencies

and harmonics of the signals. It is primarily used for modulation of demodulation of a signal.

Modulation is the translation of the signal information to a higher frequency signal, and

demodulation is the translation of signal / information carried by high frequency signal down to a

lower frequency. The principle involved in this experiment is the use of the nonlinear portion of a

transistor characteristic to mix (combine) two signals.

Below figure shows the circuit you will use in this experiment. The Vy input the local

oscillator and is made large so that the signal is cut off at the Collector. This forces the transistor

to operate in a very nonlinear region. Now that the transistor is operating in a nonlinear

regional during part of its cycle the input signal representing an input from the IF of a radio, is

introduced at a low level (millvolts). The result is an output at the collector at the transistor that

contains all the frequencies (sum, difference and high frequence harmonics) An example if Vyis

500 Khz and Vx is 520 Khsz the output frequencies at the collector will be do, dc, 20 Khz, 20

Khz, I Mhz, 1.092 MHz and other harmonics of the sum frequencies, the difference frequencies,

and the original frequencies.

In a radio you are interested only in the audio output: therefore you need to eliminate all

higher frequencies. In this circuit you are interested only in the 20 Khz signal (which is above the

usual audio range but provides a good signal on many spectrum analyzers), so you must design a

filter to eliminate all the higher frequency signals. The 500 Khz component is the largest in the

output because of the very large signal generated by the local oscillator (Vy). Thus a special

notch filter will be used to attenuate this large singnal and a low pass filter will be used to

attenuate other harmonics.



TABULAR COLOUMN:

S.NOInputs Filter Output

Vx sin (2∏fxt) Vy sin (2∏fyt) Vo sin (2∏fot)



PROCEDURE:

1. Connect the circuit as per the circuit diagram.

2. Observe the output signal of RF generator 1 and 2 using CRO and note that output voltage of RF generator 1 is approximately 3VPP (frequency between 400 to 550 KHz) and RF generator 2 is approximately 0.6VPP (frequency between 550KHz).

3. Set RF generator 1 output at 500KHz with the help of IFT and connect it to the V Y input (which represents local oscillator) of the mixer circuit.

4. Observe the signal at output using CRO. Vary the amplitude of the RF generator 1 using potentiometer until the signal at output is noticeably nonlinear (note that the signal is clipped). The clipping is necessary to introduce nonlinearities, which is how the sum and difference frequencies and other harmonics are produced.

5. Set RF generator 2 output at 520KHz with the help of IFT and connect it to the V X input (which represents IF signal) of the mixer circuit and observe the signal at mixer output using CRO.

6. Connect output of mixer to filter input and observe output signal. Note that the signal is approximately 0.7VPP of 20KHz frequency.

7. Change VX and VY signal frequencies and observe output signal.

PRECAUTIONS:

RESULT:

QUESTIONS:

1. The need for a frequency mixer is _________

2. Heterodyning is

3. ___________filter is used at the o/p of transistor circuit in a frequency mixer?

4. The frequency components that appear at the collector of the transistor in the mixer circuit are __

5. The transistor operated in the nonlinear region in a frequency mixer because ________________
