Impedance Matching and Tuning MCQs ( Microwave Engineering ) MCQs – Microwave Engineering MCQs
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Microwave Engineering MCQs – Impedance Matching and Tuning MCQs ( Microwave Engineering ) MCQs
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Impedance Matching Using Slotted Lines
1. Slotted line is a transmission line configuration that allows the sampling of:
a) electric field amplitude of a standing wave on a terminated line
b) magnetic field amplitude of a standing wave on a terminated line
c) voltage used for excitation
d) current that is generated by the source
Answer: a
Explanation: Slotted line allows the sampling of the electric field amplitude of a standing wave on a terminated line. With this device, SWR and the distance of the first voltage minimum from the load can be measured, from this data, load impedance can be found.
2. A slotted line can be used to measure _____ and the distance of _____________ from the load.
a) SWR, first voltage minimum
b) SWR, first voltage maximum
c) characteristic impedance, first voltage minimum
d) characteristic impedance, first voltage maximum
Answer: a
Explanation: With a slotted line, SWR and the distance of the first voltage minimum from the load can be measured, from this data, load impedance can be found.
3. A modern device that replaces a slotted line is:
a) Digital CRO
b) generators
c) network analyzers
d) computers
Answer: c
Explanation: Although slotted lines used to be the principal way of measuring unknown impedance at microwave frequencies, they have largely been superseded by the modern network analyzer in terms of accuracy, versatility and convenience.
4. If the standing wave ratio for a transmission line is 1.4, then the reflection coefficient for the line is:
a) 0.16667
b) 1.6667
c) 0.01667
d) 0.96
Answer: a
Explanation: ┌= (SWR-1)/ (SWR+1). Substituting for SWR in the above equation for reflection co-efficient, given SWR is 1.4, reflection co-efficient is 0.16667.
5. If the reflection coefficient of a transmission line is 0.4, then the standing wave ratio is:
a) 1.3333
b) 2.3333
c) 0.4
d) 0.6
Answer: b
Explanation: SWR= (1+┌)/ (1-┌). Where ┌ is the reflection co-efficient. Substituting for the reflection co-efficient in the equation, SWR is 2.3333.
6. Expression for ϴ means phase angle of the reflection co efficient r=|r|-e^jθ, the phase of the reflection co-efficient is:
a) θ=2π+2βLmin
b) θ=π+2βLmin
c) θ=π/2+2βLmin
d) θ=π+βLmin
Answer: b
Explanation: here, θ is the phase of the reflection co-efficient. Lmin is the distance from the load to the first minimum. Since voltage minima repeat every λ/2, any multiple of λ/2 can be added to Lmin .
7. In the expression for phase of the reflection coefficient, Lmin stands for :
a) distance between load and first voltage minimum
b) distance between load and first voltage maximum
c) distance between consecutive minimas
d) distance between a minima and immediate maxima
Answer: a
Explanation: Lmin is defined as the distance between the terminating load of a transmission line and the first voltage minimum that occurs in the transmission line due to reflection of waves from the load end due to mismatched termination.
8. If SWR=1.5 with a wavelength of 4 cm and the distance between load and first minima is 1.48cm, then the reflection coefficient is:
a) 0.0126+j0.1996
b) 0.0128
c) 0.26+j0.16
d) none of the mentioned
Answer: a
Explanation: ┌= (SWR-1)/ (SWR+1). Substituting for SWR in the above equation for reflection co-efficient, magnitude of the reflection co-efficient is 0.2. To find θ, θ=π+2βLmin, substituting Lmin as 1.48cm, θ=86.4⁰. Hence converting the polar form of the reflection co-efficient into rectangular co-ordinates, reflection co-efficient is 0.0126+j0.1996.
9. If the characteristic impedance of a transmission line 50 Ω and reflection coefficient is 0.0126+j0.1996, then load impedance is:
a) 47.3+j19.7Ω
b) 4.7+j1.97Ω
c) 0.26+j0.16
d) data insufficient
Answer: a
Explanation: ZL=Z0 (1+┌)/ (1-┌). Substituting the given values of reflection co-efficient and characteristic impedance, ZL is 47.3+j19.7Ω .
10. If the normalized load impedance of a transmission line is 2, then the reflection co-efficient is:
a) 0.33334
b) 1.33334
c) 0
d) 1
Answer: a
Explanation: ZL=Z0 (1+┌)/ (1-┌), this is the expression for load impedance. Normalized load impedance is the ratio of load impedance to the characteristic impedance, taking ZLL/Z0 as 2, the reflection co-efficient is equal to 0.33334.
Single Stub Matching
1. The major advantage of single stub tuning over other impedance matching techniques is:
a) Lumped elements are avoided
b) It can be fabricated as a part of transmission line media
c) It involves two adjustable parameters
d) All of the mentioned
Answer: d
Explanation: Single stub matching does not involve any lumped elements, it can be fabricated as a part of transmission media and it also involves to adjustable parameters namely length and distance from load giving more flexibility.
2. Shunt stubs are preferred for:
a) Strip and microstrip lines
b) Coplanar waveguides
c) Circular waveguide
d) Circulators
Answer: a
Explanation: Since microstrip and strip lines are simple structures, impedance matching using shunt stubs do not increase the complexity and structure of the transmission line. Hence, shunt stubs are preferred for strip and microstrip lines.
3. The two adjustable parameters in single stub matching are distance‘d’ from the load to the stub position, and _________
a) Susceptance or reactance provided by the stub
b) Length of the stub
c) Distance of the stub from the generator
d) None of the mentioned
Answer: a
Explanation: Reactance or susceptance of the matching stub must be known before it used for matching, since it is the most important parameter for impedance matching between the load and the source.
4. In shunt stub matching, the key parameter used for matching is:
a) Admittance of the line at a point
b) Admittance of the load
c) Impedance of the stub
d) Impedance of the load
Answer: a
Explanation: In shunt stub tuning, the idea is to select d so that the admittance Y, seen looking into the line at distance d from the load is of the form Yₒ+jb) Then the stub susceptance is chosen as –jB, resulting in a matched condition.
5. For series stub matching, the parameter used for matching is:
a) Impedance of the transmission line at a point
b) Voltage at a point on the transmission line
c) Admittance at a point on the transmission line
d) Admittance of the load
Answer: a
Explanation: In series sub matching, the distance‘d’ is selected so that the impedance, Z seen looking into the line at a distance‘d’ from the load is of the form Zₒ+jX. Then the stub reactance is chosen as –jX resulting in a matched condition.
6. For co-axial lines and waveguides, ________ is more preferred.
a) Open circuited stub
b) Short circuited stub
c) Slotted section
d) Co-axial lines cannot be impedance matched
Answer: b
Explanation: For co-axial cables and waveguides, short-circuited stub is usually preferred because the cross-sectional area of such an open-circuited line may be large enough to radiate, in which case the stub is no longer purely reactive.
7. For a load impedance of ZL=60-j80. Design of 2 single-stub shunt tuning networks to match this load to a 50Ω line is to be done. What is the normalized admittance obtained so as to plot it on smith chart?
a) 1+j
b) 0.3+j0.4
c) 0.4+j0.3
d) 0.3-j0.4
Answer: b
Explanation: To impedance match a load to a characteristic impedance of the transmission line, first the load has to be normalized. That is, zL=ZL/Z0. For impedance matching using shunt stubs, admittance is used. Taking the reciprocal of impedance, normalized load admittance is 0.3+j0.4.
8. If the normalized admittance at a point on a transmission line to be matched is 1+j1.47. Then the normalized susceptance of the stub used for shunt stub matching is:
a) 1Ω
b) 1.47 Ω
c) -1.47 Ω
d) -1 Ω
Answer: c
Explanation: When shunt stubs are used for impedance matching between a load and transmission line, the susceptance of the shunt stub must be negative of the line’s susceptance at that point for impedance matching.
9. After impedance matching, if a graph is plot with frequency v/s reflection co-efficient of the transmission line is done, then at the frequency point for which the design is done, which of the following is true?
a) There is a peak at this point of the curve
b) There is a dip at this point of the curve
c) The curve is a straight line
d) Such a plot cannot be obtained
Answer: b
Explanation: Since the plot is frequency v/s reflection co-efficient, after impedance matching the reflection co-efficient will be zero or minimum. Hence, there is a dip at that point of the curve.
10. In series stub matching, if the normalized impedance at a point on the transmission line to be matched is 1+j1.33. Then the reactance of the series stub used for matching is:
a) 1 Ω
b) -1.33 Ω
c) -1 Ω
d) 1.33 Ω
Answer: b
Explanation: The reactance of the series stub is negative of the reactance of the line at the point at which it has to be matched. That is, if the line reactance is inductive, the series stub’s reactance is capacitive.
Double Stub Tuning
1. The major disadvantage of single stub tuning is:
a) it requires a variable length of line between the load and the stub
b) it involves 2 variable parameters
c) complex calculation
d) none of the mentioned
Answer: a
Explanation: Single stub matching requires a variable length line between the stub and the load for matching which is a major disadvantage since the length of the stub plays a crucial role in matching.
2. The major advantage of double stub tuning is:
a) it uses 2 tuning stubs in fixed positions
b) it involves 2 stubs
c) length of the stub is variable
d) none of the mentioned
Answer: a
Explanation: The disadvantage of single stub tuning is overcome in double stub tuning. It uses 2 tuning stubs in fixed positions so that the length between the first stub and the load is not variable.
3. In a double stub tuner circuit, the load is of _______ length from the first stub.
a) fixed length
b) arbitrary length
c) depends on the load impedance to be matched
d) depends on the characteristic impedance of the transmission line
Answer: b
Explanation: The position of the first stub in a double stub tuner is variable from the load end. But the distance between the 2 stubs is fixed based on the value to which impedance is matched.
4. Double stub tuners are fabricated in coaxial line are connected in shunt with the main co-axial line.
a) true
b) false
Answer: a
Explanation: Most of the transmission lines used in most of the practical applications use coaxial cables, for which impedance matching of the load are done using double stub tuners which are made of coaxial cables for their best suited properties.
5. Impedance matching with a double stub tuner using a smith chart yields 2 solutions.
a) true
b) false
Answer: a
Explanation: Both single stub tuning and double stub tuning give two solutions. The intersection of the admittance and the 1+jb circle drew on the smith chart yields 2 points from which 2 solutions can be generated.
6. All load impedances can be matched to a transmission line using double stub matching.
a) true
b) false
Answer: a
Explanation: When a smith chart is used for impedance matching, if the normalized load admittance yL were inside the g+jb circle, no value of stub susceptance b1 could ever bring the load point to intersect with the 1+jb circle; this forms a forbidden range of admittance that cannot be matched.
7. The simplest method of reducing the forbidden range of impedances is:
a) increase the distances between the stubs
b) reduce the distance between the stubs
c) increase the length of the stubs
d) reduce the length of the stubs
Answer: b
Explanation: Reducing the distances between the stubs reduces the forbidden area in the smith chart which involves the load impedances that cannot be matched. Thus, more number of load impedances (range) can be matched to the transmission line.
8. Stub spacing that are near 0 and λ/2 lead to more frequency sensitive matching networks.
a) true
b) false
Answer: a
Explanation: Though theoretically the stub spacing must be small enough to reduce the forbidden area, for practical considerations, the stubs have to be placed sufficiently far enough for fabrication ease and reduce frequency sensitivity.
9. The standard stub spacing usually used is:
a) 0, λ/2
b) λ/4, λ/8
c) λ/8, 3λ/8
d) none of the mentioned
Answer: c
Explanation: While stub spacing of 0, λ/2 lead to frequency sensitive matching circuits, an optimum value of spacing is chosen taking into consideration, the various design constraints. This optimum spacing usually used is λ/8, 3λ/8.
10. If the length of the line between the first stub and the load can be adjusted, the admittance can be moved from the forbidden region.
a) true
b) false
Answer: a
Explanation: If the design requirements for impedance matching are more flexible, then the length of the line between the load and the first stub can be varied. This would result in moving the load admittance point out of forbidden region in the smith chart thus enabling impedance matching.
Quarter Wave Transformer(Smith Chart)
1. A quarter wave transformer is useful for matching any load impedance to a transmission line.
a) True
b) False
Answer: b
Explanation: Quarter wave transformers are a simple circuit that can be used to match real load impedance to a transmission line. Quarter wave transformers cannot be used to match complex load impedances to a transmission line.
2. Major advantage of a quarter wave transformer is:
a) It gives proper matching
b) It gives high gain
c) Broader bandwidth
d) None of the mentioned
Answer: c
Explanation: Quarter-wave transformers can be extended to multi section designs in a methodical manner to provide a broader bandwidth.
3. If a narrow band impedance match is required, then more multi section transformers must be used.
a) True
b) False
Answer: b
Explanation: If a narrow band impedance match is required, then a single section of quarter wave transformer is used. When a wideband impedance match is required, then multi-section quarter wave transformers must be used for impedance matching.
4. The major drawback of the quarter wave transformer that it cannot match complex load to a transmission line cannot be overcome.
a) True
b) False
Answer: b
Explanation: The major drawback of the quarter wave transformer that it cannot match complex load to a transmission line can be overcome by transforming complex load impedance to real load impedance.
5. Complex load impedance can be converted to real load impedance by:
a) Scaling down the load impedance
b) By introducing an approximate length of transmission line between load and quarter wave transformer
c) Changing the operating wavelength
d) None of the mentioned
Answer: b
Explanation: By introduction of a transmission line of suitable length between the load and the quarter wave transformer, the reactive component of the load that is the complex value can be nullified thus leaving behind only real load impedance to be matched.
Microwave Network Analysis MCQs
6. Converting complex load into real load for impedance matching has no effect on the bandwidth of the match.
a) True
b) False
Answer: b
Explanation: Adding a length of line to the transmission line between the load and quarter wave transformer alters the frequency dependence of the load thus altering the bandwidth of the match.
7. If a single section quarter wave transformer is used for impedance matching at some frequency, then the length of the matching line is:
a) Is different at different frequencies
b) Is a constant
c) Is λ/2 for other frequencies
d) None of the mentioned
Answer: a
Explanation: The length of the matching section is λ/4 for the frequency at which it is matched. For other frequencies, the electrical length varies. For multi section transformers, a wide bandwidth can be achieved.
8. Quarter wave transformers cannot be used for non-TEM lines for impedance matching.
a) True
b) False
Answer: a
Explanation: For non-TEM lines, propagation constant is not a linear function of frequency and the wave impedance is frequency dependent. These factors complicate the behavior of the quarter wave transformer for non-TEM lines.
9. The reactances associated with the transmission line due to discontinuities:
a) Can be ignored
b) Have to matched
C Discontinuities do not exist
d) None of the mentioned
Answer: b
Explanation: Reactance due to discontinuities in the transmission line contribute to the impedance, they can be matched by altering the length of the matching section.
10. If a load of 10Ω has to be matched to a transmission line of characteristic impedance of 50Ω, then the characteristic impedance of the matching section of the transmission line is:
a) 50Ω
b) 10Ω
c) 22.36Ω
d) 100Ω
Answer: c
Explanation: Characteristic impedance of the matching section of a transmission line is given by Z1=√Zₒ.ZL. Substituting the given impedance values, the characteristic impedance of the matching section is 22.36 Ω.
Reflections
1. Discontinuities in the matching quarter wave transformer are not of considerable amount and are negligible.
a) True
b) False
Answer: b
Explanation: Discontinuities in the matching network cause reflections which result in considerable attenuation of the transmitted signal. Hence, discontinuities in transformers are not negligible.
2. The overall reflection coefficient of a matching quarter wave transformer cannot be calculated because of physical constraints.
a) True
b) False
Answer: b
Explanation: Though the computation of total reflection is complex, the total reflection can be computed in two ways. They are the impedance method and the multiple reflection method.
3. In the multiple reflections analysis method, the total reflection is:
a) An infinite sum of partial reflections
b) An infinite sum of partial reflection and transmissions
c) Constant value
d) Finite sum of partial reflections
Answer: b
Explanation: The number of discontinuities in the matching circuit (quarter wave transmission line) is theoretically infinite since the exact number cannot be practically determined. Hence, the total reflection is an infinite sum of partial reflections and transmission.
4. The expression for total reflection in the simplified form is given by:
a) Г=Г1+ Г3e-2jθ
b) Г=Г11+Г3
c) Г=Г12+ Г3e-2jθ
d) Г= Г1+ Г2e-2jθ
Answer: a
Explanation: This expression dictates that the total reflection is dominated by the reflection from the initial discontinuity between Z1 and Z2 (Г1), and the first reflection from the discontinuity between Z2 and ZL (Г3e-2jθ).
5. The e-2jθ term in the expression for total reflection in a single section quarter wave transformer impedance matching network Г=Г1+ Г3e-2jθ signifies:
a) Phase delay
b) Frequency change
c) Narrowing bandwidth
d) None of the mentioned
Answer: a
Explanation: The term e-2jθ in Г=Г1+ Г3e-2jθ accounts for phase delay when the incident wave travels up and down the line. This factor is a result of multiple reflections.
6. If the first and the third reflection coefficients of a matched line is 0.2 and 0.01, then the total reflection coefficient if quarter wave transformer is used for impedance matching is:
a) 0.2
b) 0.01
c) 0.21
d) 0.19
Answer: d
Explanation: The total reflection co-efficient of a matched line due to discontinuities is given by Г=Г1+ Г3e-2jθ. Given that Г1=0.2 and Г3=0.01, β=2π/λ, l=λ/4. θ=βl, Substituting the given values in the above 2 given equations, the total reflection coefficient is 0.19.
7. If a λ/4 transmission line is used for impedance matching, then always Г1> Г3.
a) True
b) False
Answer: a
Explanation: Since the load is matched to the transmission line the reflection from the load towards the source will be very less (Г3). Г1 is the reflection from the junction of the transmission line and the λ/4 matching section. Since this end will have some improper matching and discontinuities, Г1 is always greater than Г3.
8. To compute the total reflection of a multi-section transmission line, the lengths of the transmission lines considered are all unequal.
a) True
b) False
Answer: b
Explanation: The computation of total reflection of a matched line due to discontinuities is theoretically complex. In order to obtain an approximated simple expression, the lengths of the multi section matching transformers is a constant or all of them are equal.
9. If ZL< Z0, then the reflection coefficient at that junction is:
a) ГN<0
b) ГN>0
c) ГN>1
d) None of the mentioned
Answer: a
Explanation: When there is no proper matching between load impedance and the characteristic impedance of a transmission line and given the condition that ZL< Z0, then the reflection coefficient at that junction is always negative. That is, ГN<0.
10. The total approximate reflection coefficient is a finite sum of reflection co-efficient of individual matching section of the matching network.
a) True
b) False
Answer: a
Explanation: In a multi section transformer there are N sections, if the reflection from each section is ГN, then the total reflection is the sum of reflections that occur due to individual sections. There is an exponential component associated with each reflection coefficient that decays exponentially.
11. Using the relation for total reflection co-efficient certain designs of matching networks can be made as per practical requirements.
a) True
b) False
Answer: a
Explanation: We can synthesize any desired reflection coefficient response as a function of frequency by properly choosing the ГN and using enough sections (N).
Binomial Multi-section Matching Transformers
1. The passband response of a binomial matching transformer can be called optimum:
a) if the roll off in the response curve is high
b) if the response is flat in the impedance matched region
c) if the matching network is frequency sensitive
d) none of the mentioned
Answer: B
Explanation: The response curve of a binomial matching transformer ( θ v/s │Г (θ) │) must be flat at the frequency for which impedance matching is performed and for those frequencies that lie in the required bandwidth. This is one of the most important characteristic of a good matching circuit.
2. If a quality binomial matching transformer gives a good flat response curve, it is called “maximally flat”.
a) true
b) false
Answer: A
Explanation: A binomial matching section can be termed efficient when it is less frequency sensitive and gives a constant gain over a wide range of frequencies. This constant gain implies a flat curve over a wide range of frequencies. This is termed as “maximally flat”.
3. The response curve of a binomial matching transformer is plotted for each section of the matching network individually and then analyzed for optimum solution.
a) true
b) false
Answer: B
Explanation: The response curve of a binomial multisection transformer is determined for an N-section transformer by setting the first N-1 derivatives of │Г (θ) │ to zero at the center frequency, fₒ.
4. To obtain a flat curve in the response of a binomial multisection transformer, N-1 derivatives of │Г (θ) │are set to zero. This implies:
a) the frequency sensitivity of the matching section is increased linearly
b) the frequency sensitivity of the matching section is increased exponentially
c) roll off in the curve is increased
d) none of the mentioned
Answer: D
Explanation: The derivatives of │Г (θ) │ show the rate of change of reflection co-efficient with distance. If this derivative is not zero, the matching circuit becomes more sensitive and a higher bandwidth cannot be obtained. Hence to make the matching network frequency independent, the derivatives are set to zero.
5. The condition │Г (θ) │=0 for θ=π/2 of a binomial multi section transformer corresponds to the:
a) upper cutoff frequency
b) lower cutoff frequency
c) center frequency
d) none of the mentioned
Answer: C
Explanation: θ=π/2 corresponds to the center frequency at which │Г (θ) │=0. θ=βl. β=2 π/λ and l=λ/4. Substituting for β and λ in the equation for θ, θ=π/2. This is the center frequency at which impedance matching is done at which the reflection coefficient is zero and perfect match is achieved.
6. The reflection co-efficient magnitude of a binomial multisection transformer is:
a) 2N│A││cos (θ)│N
b) 2N│A│
c) 2N│cos (θ) │N
d) none of the mentioned
Answer: A
Explanation: The reflection co-efficient of a binomial multisection transformer is dependent on the length of the matching section, operating frequency and load impedance and characteristic impedance. A is a constant defined as A=2-N (ZL– Z0)/ (ZL+ Z0).
7. The reflection coefficient ГN in terms of successive impedances Zn and Zn+1 when multisection transformers are used in a binomial matching transformer is given by:
a) 0.5ln (Zn+1/Zn)
b) ln (Zn+1/Zn)
c) 0.5ln (Zn/Zn+1)
d) (Zn/Zn+1)
Answer: A
Explanation: After binomial expansion of the equation for Г(θ), the maximum power is N, where N is the number of the sections in the transformer. After making suitable approximations so that the approximated values are in well agreement with actual values, the expression for reflection coefficient is 0.5ln (Zn+1/Zn).
8. In the plot of normalized frequency v/s reflection co-efficient for a binomial multisection filter, the curve has a dip at:
a) center frequency
b) upper cutoff frequency
c) lower cutoff frequency
d) none of the mentioned
Answer: A
Explanation: Since the impedance matching circuit is used to match the load to the transmission line, there will be perfect match in the circuit resulting in zero or low reflection. Hence, there is a dip at the center frequency.
9. As the number of sections in the binomial multisection transformer increases the plot of normalized frequency v/s reflection co-efficient has a wider open curve.
a) true
b) false
Answer: A
Explanation: When more number of sections are used for matching, the reflection co-efficient is low for neighboring frequencies as well. Hence, the network can be used for a wide range of operating frequencies. Hence, this increases the bandwidth.
10. A three section binomial transformer is used to match a 100Ω transmission line to a 50Ω transmission line. Then the value of the constant ‘A’ for this design is:
a) -0.0433
b) 0.0433
c) 0.01
d) -0.01
Answer: A
Explanation: ‘A’ is given by the expression 2-(n+1)ln (ZL/Z0), Where N is the number of sections in the matching network. Substituting the given values in the equation for ‘A’, the value of A is -0.0433.
Chebyshev Multi-section Matching Transformers
1. The major disadvantage of binomial multi section transformer is higher bandwidth cannot be achieved.
a) true
b) false
Answer: a
Explanation: In some applications, a flat curve in the operating frequency is a major requirement. This requirement can be satisfied using a binomial transformer. But the disadvantage is that a higher bandwidth can be achieved.
2. Advantage of chebyshev matching transformers over binomial transformers is:
a) higher gain
b) low power losses
c) higher roll-off in the characteristic curve
d) higher bandwidth
Answer: d
Explanation: Chebyshev transformers when designed to operate at a certain frequency called center frequency, the reflection co-efficient is low for a large frequency range implying that they have a higher operating range. This is the major advantage of chebyshev filters.
3. There are passband ripples present in the chebyshev characteristic curve.
a) true
b) false
Answer: a
Explanation: This is a major difference between chebyshev and binomial transformer. Binomial transformers have a flat curve in the passband while chebyshev transformers have ripples in the transformer passband.
4. Chebyshev matching transformers can be universally used for impedance matching in any of the microwave networks.
a) true
b) false
Answer: b
Explanation: Chebyshev transformers have passband ripples in the characteristic curve. In some critical applications, these ripples are not tolerable in the operating bandwidth. Hence, chebyshev transformers cannot be used for all the microwave networks for impedance matching.
5. The 4th order chebyshev polynomial is:
a) 8x4-8x2+1
b) 4x3-4x2+1
c) 4x3-3x
d) none of the mentioned
Answer: a
Explanation: nth order polynomial for a chebyshev polynomial is generated using lower polynomials by the expression Tn (x) = 2xTn-1(x) – Tn-2(x). T2(x) = 2x2-1, T3(x)= 4x3-3x. Substituting the lower level polynomials in the given expression, T4(x) = 8x4-8x2+1.
6. Chebyshev polynomials do not obey the equal-ripple property.
a) true
b) false
Answer: b
Explanation: For -1≤x≤1,│T(x)│≤ 1. In this range, the chebyshev polynomials oscillate between±1. This is the equal ripple property. Chebyshev polynomials obey the equal-ripple property.
7. Chebyshev polynomial can be expressed in trigonometric functions as:
a) Tn(cos θ)=cos nθ
b) Tn(sin θ)= sin nθ
c) Tn(cos θ)=cos nθ.sin nθ
d) none of the mentioned
Answer: a
Explanation: If the chebyshev polynomial variable x is equated to a trigonometric variable cos θ, then the higher order chebyshev polynomials can be defined in terms of the same function with multiples of θ. This can be theoretically proved and function generation becomes simpler.
8. For values of x greater than 1, the chebyshev polynomial in its trigonometric form cannot be determined.
a) true
b) false
Answer: b
Explanation: Since cosine function is defined for values of x between -1 and +1, for x values greater than 1, hyperbolic function is used to define the chebyshev polynomial. Tn(x)=cosh (n cosh-1x).
9. Reflection co-efficient Гn in terms of Zn and Zn+1, successive impedances of successive sections in the matching network are:
a) 0.5 ln (Zn+1/Zn)
b) 0.5 ln (Zn/Zn+1)
c) ln (Zn+1/Zn)
d) ln (Zn/Zn+1)
Answer: a
Explanation: When multiple sections are used in the chebyshev matching network, the reflection co-efficient of the nth matching section, given the impedances at the ends of the section, reflection co-efficient can be obtained using the expression 0.5 ln (Zn+1/Zn).
10. In a 3 section multisection chebyshev matching network, if Z3 = 100Ω, and Z2=50Ω, then the reflection co-efficient Г2 is:
a) 0.154
b) 0.3465
c) 0.564
d) none of the mentioned
Answer: b
Explanation: Гn for ‘n’ section matching chebyshev network is given by Гn=0.5 ln (Zn+1/Zn). substituting the given values in the expression, Г2 is 0.3465.
11. If Г3=0.2 and Z3=50Ω, then the impedance of the next stage in the multi-section transformer is:
a) 100Ω
b) 50Ω
c) 74.6Ω
d) 22.3Ω
Answer: c
Explanation: Гn for ‘n’ section matching chebyshev network is given by Гn=0.5 ln (Zn+1/Zn). Substituting the given values in the expression, the impedance of the next stage is Z4=74.6Ω.
Tapered Lines
1. A single section tapered line is more efficient in impedance matching than a multisection tapered line for impedance matching.
a) True
b) False
Answer: b
Explanation: As the number N of discrete transformer sections increases, the step changes in the characteristic impedance between the sections become smaller, and the transformer geometry approaches a continuous tapered line. Thus multisection are preferred over single section for impedance matching.
2. Passband characteristics of tapered lines differ from one type of taper to another.
a) True
b) False
Answer: a
Explanation: The impedance of the tapered line varies along the line depending on the type of the tapering done. Thus impedance is a function of the type of taper. Hence passband characteristics depend on the type of taper.
3. For a continually tapered line, the incremental reflection co-efficient is:
a) ∆Z/2Z
b) 2Z/∆Z
c) ∆Z0/2Z0
d) None of the mentioned
Answer: a
Explanation: The incremental reflection co-efficient ∆Г is a function of distance. If a step change in impedance occurs for z and z+∆z, then the incremental reflection co-efficient is given by ∆Z/2Z.
4. The variation of impedance of an exponentially tapered line along the length of the line is given by:
a) Z(z)=Z0eaz
b) Z(z)=Z0e-az
c) Z(z)=Z0e2az
d) Z(z)=Z0e-2az
Answer: a
Explanation: The variation of impedance along the transmission line is a positive growing curve and is given by Z(z)=Z0eaz. The constant ‘a’ is defined as L-1 ln(ZL/Z0).
5. The value of constant ‘a’ for an exponentially tapered line of length 5 cm with load impedance being 100Ω and characteristic impedance of the line is 50Ω is:
a) 0.1386
b) 0.265
c) 0.5
d) 0.2
Answer: a
Explanation: The constant ‘a’ for a tapered transmission line is given by L-1 ln(ZL/Z0). ‘a’ is a function of the tapered length, load and characteristic impedance. Substituting the given values in the above expression, ‘a’ has the value 0.1386.
6. Reflection co-efficient magnitude response is an exponential curve for tapered line.
a) True
b) False
Answer: b
Explanation: The reflection co-efficient magnitude response of a exponential tapered line resembles only positive valued sinc function or can be called as a function with multiple peaks.
7. Triangular taper is the best solution for any impedance matching requirement.
a) True
b) False
Answer: b
Explanation: Klopfenstein taper is the best and most optimized solution for impedance matching because reflection co-efficient has minimum value in the passband.
8. The maximum passband ripple in a Klopfenstein taper matching section is:
a) Г0/cos h A
b) Г0/sin h A
c) Г0/ tan h A
d) None of the mentioned
Answer: a
Explanation: The maximum passband ripple in a Klopfenstein taper matching section is Г0/cos h A. Here, Г0 is the reflection co-efficient at zero frequency. A is a trigonometric function relating reflection co-efficient at zero frequency and maximum ripple in the passband.
9. For any load impedance, perfect match can be obtained and the minimum reflection co-efficient achieved can be zero.
a) True
b) False
Answer: b
Explanation: From Bode-Fano criterion, there is a theoretical limit on the minimum achievable reflection co-efficient for a given load impedance. Hence, perfect match cannot be obtained.
10. For a given load (a fixed RC product), a broader bandwidth can be achieved with a low reflection co-efficient in the passband.
a) True
b) False
Answer: b
Explanation: Based on the theoretical results of Bode-Fano criterion, a broader bandwidth can be achieved only at the expense of a higher reflection coefficient in the passband.
11. A perfect match can be obtained in the passband for any impedance matching circuit around the center frequency for which it is defined.
a) True
b) False
Answer: b
Explanation: The passband reflection co-efficient cannot be zero unless the bandwidth is zero. Thus a perfect match can be obtained only at a finite number of discrete frequencies.