Z Parameters MCQ Quiz in தமிழ் - Objective Question with Answer for Z Parameters - இலவச PDF ஐப் பதிவிறக்கவும்

Concept:

The z parameters of a two-port network is defined as:

V₁ = z₁₁ I₁ + z₁₂ I₂

V₂ = z₂₁ I₁ + z₂₂ I₂

Calculation:

z₁₁ and z₂₁ parameters are calculated by open circuiting the output (i.e. I₂ = 0)

The circuit given will be redrawn as:

With i₂ = 0

From the above, we see that I₁ = 0

So, 

V₁ = 10 I₁ - 6 I₂        ____ (1)

V₂ = -4 I₁ + 12 I₂         _____ (2)

V₂ = -10 I₂        ____ (3)

Convert the current source to voltage source.

:

12 - 6 I₁ - V₁ = 0

V₁ = 12 - 6 I₁ ____ (4)

Substitute equation (3) and (4) in (1) and (2)

12 - 6I₁ = 10 I₁ - 6 I₂

12 = 16 I₁ - 6 I₂       ____ (5)

-10 I₂ = -4 I₁ + 12 I₂

0 = -4 I₁ + 22 I₂      ____(6)

From 5 and 6

I₁ = 0.8049 A

I₂ = 0.1463 A

Z-parameters:

Z-parameters are also known as the Open-Circuit impedance parameters as they are calculated under open-circuit conditions, i.e. at I1 = 0 and I2 = 0, In the matrix form, they are expressed as:

V1 = z11I1 + z12I2

V2 = z21I1 + z22I2

With the input open-circuited, i.e. I1 = 0, the two parameters obtained are:

With the output open-circuited, i.e. I2 = 0, the two parameters we obtain are:

Concept:

The condition in the symmetrical T network is that the total series arm impedance and shunt arm impedance must be z₁ and z₂ respectively.

Analysis:

We know;

Z-parameter;

V₁ = Z₁₁ I₁ + Z₁₂ I₂       ---(1)

V₂  = Z₂₁ I₁ + Z₂₂ I₂      ---(2)

        ---(3)

       ---(4)

From (1), (2), (3), (4)

∴Z₂₁ = Z₁₂

Z11 = Z22

Concept:

Z-parameters are also known as the Open-Circuit impedance parameters as they are calculated under open-circuit conditions, i.e. at I1 = 0 and I2 = 0, In the matrix form, they are expressed as:

V1 = z11I1 + z12I2

V2 = z21I1 + z22I2

Calculation:

From Z-parameters:

V₁ = 4I₁ + I₂       ---(1)

V₂ = I₁ + 2I₂       ---(2)

From (2):

– I₂ = I₁ + 2I₂

3I₂ = -I₁

    ---(3)

From (1):

∴ Resistance seen by the voltage source is:

Apply nodal analysis at V₂,

      ----(1)

     ----(2)

By solving equations (1) and (2)

⇒ 2V₂ - V₁ = α (V₁ - V_2­)

Calculation:

Applying KCL at V_A

V₁ - V_A + 2V₂ - V_A = 0

V₁ + 2V₂ = 2V_A      ---(1)

I₂ = V₂ - V_A

I₂ = V₂ – 0.5 V₁ – V₂

0.5 V₁ = - I₂

V₁ = 0I­₁ – 2I₂  ---- (1)

Applying KCL to find I₁, we get

I₁ = V₁ + V₁ - V_A

= 2V₁ – 0.5 V₁ – V₂

I₁ = 1.5 V₁ – V₂

∴ V₂ = 1.5 V₁ – I₁

= 1.5(-2 I₂) – I₁

V₂ = -3I₂ – I₁ ---- (2)

= -I₁ – 3I₂

∴ 

= 

Concept:

Z parameters:

V1 = Z11 I1 + Z12 I2

V2 = Z21 I1 + Z22 I2

 is the input driving point impedance or open circuit input impedance

 is the open circuit transfer impedance from port 1 to port 2

is the open circuit transfer impedance from port 2 to port 1

 is the output driving point impedance or open circuit output impedance

Calculation:

Apply Nodal at A, we get:

   ---(1)

With I₁ = 0,

V₂ = 2I₂

Z₂₂ = 2

With I₂ = 0,

V₂ = -2I₁

Z₂₁= -2

And from the figure we get:

Concept:

The z-parameter equations for a two-port network is given by:

V₁ = z₁₁ I₁ + z₁₂ I₂

V₂ = z₂₁ I₂ + z₂₂ I₂

Where the voltages and current can be in phasors as well.

Application:

V₁ = 100 ∠0

And V₂ = -10 I₂

Where bold letter V/I represents the phasor voltage and current respectively.

Substituting V₁ and V₂ in the standard 2-port z-parameter equations, we get:

100 = 40 I₁ + j20 I₂      ---(1)

-10 I₂ = j30 I₁ + 50 I₂

-60 I₂ = j30 I₁

Substituting I₂ in equation (1), we get:

⇒ 100 = 40 I₁  + 10I₁

I₂ = 1∠-90° A