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Experiment TW 1Experiment TW 1Experiment TW 1Experiment TW 1.2.2.2.2 –––– Characteristic impedance for long line modelsCharacteristic impedance for long line modelsCharacteristic impedance for long line modelsCharacteristic impedance for long line models

Objective: To determine characteristic impedance for a long line from short-circuit and open-

circuit measurements Theory: Under the assumption of lossless lines and where ∞=2Z (open-circuit

termination) for the input impedance ∞,1Z it follows that:

)tan(,1 lj

ZZ c

β=∞ (6)

For 02 =Z (short-circuit termination) the input impedance is given by:

)tan(0,1 lZjZ c β= (7)

Thus through conversion the characteristic impedance from ∞,1Z and 0,1Z can be

determined:

∞= ,10,1 .ZZZc (8)

Equation (8) derived for lossless lines also applies for real, lossy lines. In general

0,1Z and ∞,1Z will be complex input impedances, i.e. a phase angle which does not

equal 00 appears between the current and voltage at the input of the line. Thus, in general, the characteristic impedance cZ will also be a complex impedance. In the

following experiment only the magnitude of the characteristic impedance is measured.

Procedure:

Determining cZ for a long line model

The experiment set-up is as specified in Fig. 1-1.

1. As the measuring object use the section with 5=l km and 4.0=Φ mm from the line model II. Feed an input voltage of 2RMSV .

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Figure 1-1: Experiment Set-up

(1) Power supply (2) Frequency generator (3) Function generator (4) Object under test with STE elements

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2. Vary the frequency of the function generator according to the values from

Table 1.2-1. Record the measurements both for short-circuit and open-circuit line outputs. Enter the effective values of 1U and RU into Table 1.2-1.

3. Since the following is true for the current1I at the line input

Ω=

3001RU

I (9)

For the input impedance ∞,1Z it follows that:

Ω==∞ 300.1

1

1,1

RU

U

I

UZ (10)

4. ∞,1Z can correspondingly be determined from the voltages 1U and RU for

short-circuit Ω= 02Z on the output side. Enter your results for ∞,1Z and 0,1Z

into Table 1.2-1. Using equation (8) calculate the magnitude of the characteristic impedancecZ for each frequency.

5. Plot the characteristic )( fZZ cc = over the frequency in Figure 1-2.

Determine the optimum line termination optZ2 for the mid frequency of the

telephone band (f = 1000 Hz).

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Table 1.2-1: Determining characteristic impedance cZ from the measurement of the line’s

input impedance 1Z for open-circuit and short-circuit line termination. Line Section: Wire Diameter 4.0=φ mm

Line Length 5=l km f

(Hz) 1U

(m RMSV ) RU

(m RMSV ) ∞,1Z

( Ω ) 1U

(m RMSV ) RU

(m RMSV ) 0,1Z

( Ω ) cZ

( Ω )

100

200

300

400

500

600

800

1 000

2 000

3 000

4 000

5 000

6 000

8 000

10 000

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Figure 1-2