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Right choice is (d) C1R0^2

The EXPLANATION is: An INVERSE network is OBTAINED by converting each capacitance C into an inductance of value CR0^2 where R0 is RESISTANCE. The value of inductance L1^‘ after converting the capacitance into an inductance is L1^‘ = C1R0^2.

The correct OPTION is (c) L1/R0^2

To elaborate: An inverse network MAY be OBTAINED by converting Each inductance L should be converted into a CAPACITANCE of VALUE L/R0^2 to obtain the inverse network. The value of capacitance C1^‘ after converting the inductance into a capacitance is L1/R0^2. C1^’ = L1/R0^2.

The correct option is (a) CR0^2

The best I can explain: An INVERSE NETWORK is OBTAINED by CONVERTING each capacitance C into an inductance of value CR0^2 where R0 is resistance.

Correct answer is (a) R0^2/R

The best EXPLANATION: To obtain the INVERSE NETWORK we have to convert each RESISTANCE element R into a corresponding resistive element of value R0^2/R.

Right option is (B) L/R0^2

The explanation: An inverse NETWORK may be obtained by converting each INDUCTANCE L should be CONVERTED into a capacitance of value L/R0^2 to obtain the inverse network.

The correct option is (C) Converting each PARALLEL BRANCH into ANOTHER series branch

To explain: An inverse NETWORK may be obtained by converting each parallel branch into another series branch and vice-versa and not by converting each series branch into another series branch and not by converting each series branch into another parallel branch.

Correct choice is (d) Z1Z2 = R0^2

To elaborate: The impedances Z1 and Z2 are said to be INVERSE if the geometric MEAN of the TWO impedances is a REAL number.

The CORRECT choice is (a) R1 = R0(N-1)/(N+1)

The EXPLANATION is: R0 = R1+(R1+R0)/N. On SOLVING, the value of R1 in terms of R0 and N is R1 = R0(N-1)/(N+1).

Correct OPTION is (b) R1+ R2(R1+R0)/(R1+R0+R2)

The BEST I can EXPLAIN: The value of the characteristic impedance R0 in TERMS of R1 and R2 and R0 when it is terminated in a load of R0 is R0=R1 + R2(R1+R0)/(R1+R0+R2).

Right answer is (B) (R1+R2+R0)/R2

To EXPLAIN I WOULD SAY: R2(I1-I2)=I2(R1+R0)

=>I2(R2+R1+R0)I1R2. On solving, I1/I2=(R1+R2+R1)/R2.

Right choice is (c) (R1+R2+R0)/R2

To explain: N =I1/I2. We GOT I1/I2 = (R1+R2+R1)/R2. So on substituting we GET N = (R1+R2+R0)/R2.

The correct option is (c) N = ANTI LOG(DB/20)

Explanation: The VALUE of N in dB can be EXPRESSED as N = anti log(dB/20).

The CORRECT OPTION is (c) 20 LOG10 (N)

The EXPLANATION is: The value of one decibel is equal to 20 log10 (N). One decibel = 20 log10 (N) where N is the attenuation.

The correct CHOICE is (a) 20 log10 (V1/V2)

For explanation I would SAY: If V1 is the voltage at PORT 1 and V2 is the voltage at port 2, then the ATTENUATION in dB is Attenuation in dB = 20 log10 (V1/V2) where V1 is the voltage at port 1 and V2 is the voltage at port 2.

Right choice is (d) 20 log10 (I1/I2)

To explain I WOULD say: ASSUMING I1 is the input current and I2 is the output current leaving the PORT, the ATTENUATION in dB is Attenuation in dB = 20 log10 (I1/I2) where I1 is the input current and I2 is the output current leaving the port.

Correct choice is (B) 10 log10 (P1/P2)

To elaborate: The INCREASE or DECREASE in power DUE to insertion or SUBSTITUTION of a new element in a network can be conveniently expressed in decibels or in nepers. The attenuation in dB in terms of input power (P1) and output power (P2) is Attenuation in dB = 10 log10 (P1/P2).

Right answer is (C) 0.416

To explain: m=√(1-(FC/fr)^2) fc = 1000, fr = 1100. On SUBSTITUTING m=√(1-(1000/1100)^2)=0.416.

Right ANSWER is (a) 400

The best EXPLANATION: The VALUE of K is EQUAL to the design impedance. Given design impedance is 400Ω. So, k = 400.

The correct choice is (C) m=√(1-(fc/fr)^2)

To EXPLAIN I would say: As fr=fc/√(1-m^2). The expression of m of the m-derived low PASS FILTER is m=√(1-(fc/fr)^2).

The correct option is (a) fc/√(1-m^2)

To explain: If a sharp cut-off is DESIRED, the FREQUENCY at INFINITY should be near to fc. The resonant frequency of m-derived low PASS FILTER in terms of the cut-off frequency of low pass filter is fr=fc/√(1-m^2).

The correct option is (B) 1/(π√LC)

The best I can EXPLAIN: To DETERMINE the cut-off FREQUENCY of the low pass filter we place m = 0. So fc=1/(π√LC).

Correct CHOICE is (d) fr=1/(√(πLC(1-m^2)))

To explain I would say: ωr^2 = 1/(LC(1-m^2)). So the VALUE of resonant frequency in the m-derived LOW pass filter is fr=1/√(πLC(1-m^2)).

The CORRECT answer is (c) Zoπ = Zoπ^’

For explanation: The characteristic IMPEDANCES of the PROTOTYPE and its modified sections have to be equal for matching. The RELATION between Zoπ and Zoπ^‘ is Zoπ = Zoπ^’.

Right CHOICE is (d) Z2^‘=Z1/4 m (1-m^2)+Z2/m

For explanation: As ZOT = ZoT^’, √(Z1^2/4+Z1Z2)=√(m^2 Z1^2/4+m Z2^‘). On SOLVING, Z2^‘=Z1/(4 m (1-m^2))+Z2/m.

Right answer is (a) ZoT = ZoT^‘

The BEST explanation: The relation between ZoT and ZoT^’ is ZoT = ZoT^’ where ZoT^’ is the CHARACTERISTIC IMPEDANCE of the MODIFIED (m-derived) T-network.

The correct answer is (d) 0

Easy EXPLANATION: We KNOW that in the pass BAND, the condition is -1 < Z1/4Z2 < 0. So α = π.

Right CHOICE is (C) α=2 cosh^-1⁡(f/fc)

EASY EXPLANATION: α = 2 cosh^-1[Z1/4Z2] and Z1/4Z2 =f/fc. On substituting we get α = 2 cosh^-1⁡(f/fc).

Right option is (B) π

The explanation: We KNOW that in the attenuation band, Z1/4Z2 < -1 i.e., f/fc < 1. So the VALUE of β in the pass band of constant k-low pass FILTER is β = π.

Right choice is (b) 1/(π√LC)

To explain I WOULD say: Z1/4Z2 = 0. Z1 = jωL and Z2 = 1/jωC. On solving the cut-off FREQUENCY of the constant k-low pass FILTER is fc = 1/(π√LC).

The correct ANSWER is (b) √((L/C))

Easy explanation: We GOT Z1Z2 = L/C. And we know Z1Z2= K^2. So k^2 = L/C. So the VALUE of k is √(L/C).

The correct CHOICE is (c) 1/jωC

Best EXPLANATION: From the prototype T SECTION and prototype π section shown in figures, we get the VALUE of Z2 is 1/jωC.

Correct option is (b) Z1Z2 = k^2

To elaborate: Z1,Z2 are inverse if their product is a CONSTANT, independent of frequency, k is REAL constant, that is the resistance. k is often TERMED as design impedance or nominal impedance of the constant k-filter.

Right option is (a) jωL

To explain I would SAY: The constant K, T or π type filter is also known as the prototype because other more complex NETWORKS can be derived from it. From the given figure, the value of Z1 is jωL.

Correct CHOICE is (B) Zoπ = Z1Z2/ZoT

Best explanation: The characteristic impedance of a symmetrical π-section can be expressed in TERMS of T. Zoπ = Z1Z2/ZoT.

Right option is (d) α=2 cosh^-1⁡√(Z1/4 Z2)

To explain: If the VALUE of β is π, cos β/2 = 0. So SIN β/2 = ±1; cosh α/2 = x = √(Z1/4 Z2). This solution is valid for negative Z1/4 Z2 and having magnitude greater than or equal to UNITY. -α &LT= Z1/2 Z2 <= -1. α=2 cosh^-1⁡√(Z1/4 Z2).

The CORRECT choice is (a) 0

For explanation I WOULD SAY: As sinhα/2cos⁡β/2=0 and coshα/2 sin⁡β/2=x, the value of α if Z1, Z2 are same type of reactance is α = 0.

The correct ANSWER is (d) sinhα/2cos⁡β/2=0

For explanation I would say: If Z1, Z2 are same type of REACTANCE, then the real PART of sinhϒ/2 = sinhα/2cos⁡β/2 + jcoshα/2sin⁡β/2 should be zero. So sinhα/2cos⁡β/2=0.

Right CHOICE is (c) |Z1/4 Z2| > 0

Easiest explanation: If Z1 and Z2 are same TYPE of reactances, then √(Z1/4 Z2) should be always POSITIVE implies that |Z1/4 Z2| > 0.

Correct ANSWER is (a) α = sinh^-1⁡√(Z1/4 Z2)

EASIEST explanation: Z1, Z2 are same TYPE of reactance and |Z1/4 Z2| is real. |Z1/4 Z2| > 0. The value of α is α = sinh^-1⁡√(Z1/4 Z2).

Correct choice is (b) ϒ = α+ jβ

The best explanation: We know that the PROPAGATION constant is a complex function and the real part of the complex propagation constant is a measure of the CHANGE in magnitude of the current or voltage in the NETWORK known as ATTENUATION constant and imaginary part is a measure of the difference in phase between the INPUT and output currents or voltages known as phase shift constant. ϒ = α + jβ.

The correct choice is (C) sinh⁡ϒ/2=√(Z1/4Z2)

Best explanation: sinhϒ/2=√((1/2(coshϒ-1)/(1/2(1+Z1/2Z2-1))). The VALUE of sinh⁡ϒ/2 in terms of Z1 and Z2 is sinh⁡ϒ/2=√(Z1/4Z2).