# NEXT and FEXT crosstalk calculations

For a lossless line:

The characteristic impedance is given by Zo=sqrt(L/C) and the velocity of propagation by Vp=1/(sqrt(L*C))

Where L and C are, respectively, the line's inductance and capacitance per metre length.

A transmission line is formed by two identical parallel tracks in a printed circuit board, as depicted in the attached figure. The line has a length of 50 mm and all line terminations are of 70 . The line can be assumed to be lossless.

a) Use equations (1) and (2) to calculate the magnitude of the NEXT and FEXT voltages generated in the victim conductor when the source voltage, Vin, in the aggressor conductor is a voltage step of 2 V with a rise time of 100 ps.

[Note that the Vs voltage at the input to the aggressor conductor is

Vs=Vin(Rin/Rin+Zo)]. Please see attached drawing.

Equations:

NEXT

The crosstalk voltage appearing at the near end of the victim circuit due to a changing voltage Vs(t) in the aggressor circuit is given by:

Vne=Kne[Vs(t)-Vs(t-2td)]............(1a)

Kne=1/4td(C*Zo+L/Zo)...............(1b)

Kne is the near end coupling coefficient and C and L are the per unit length mutual capacitance and inductance respectively and td is the time taken for the aggressor signal to travel down the line.

FEXT

The crosstalk voltage generated at the far end of the victim circuit due to a changing voltage Vs(t) in the aggressor circuit is given by:

Vfe=Kfe*l*d/dt[Vs(t-td)]...............(2a)

where l is the length of the line

Kfe=1/2(C*Zo-L/Zo.....................(2b)

b) Sketch the NEXT and FEXT waveforms.

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#### Solution Preview

Please see the 2 attachments for the solution.

- Near End Cross Talk NEXT voltage analysis

The NEXT voltage is given by 1a.

1a.

where is given by 1b.

1b.

However, since the characteristic impedance of the transmission line is given by the square root of the ratio of unit length line inductance and unit length line capacitance we can write and the velocity of propagation of signals along the line given by which on substitution into 1b yields the alternative simplified form for given by equation1c as shown below.

1c.

We can evaluate these ratios since we are given the unit length mutual inductance between the lines as and the unit length line inductance as so

In addition as we are given the unit length mutual capacitance between the lines as and the unit length line capacitance as so we can evaluate the ratio

Then

Also we need to evaluate using the parameter values given where

Then

Since

And

We can also work out the velocity ...

#### Solution Summary

The expert examines NEXT and FEXT crosstalk calculations.

Multiple electrical signal, level, noise calcualtions

1. FIGURE 1 shows the block diagram of a superhetrodyne radio receiver. In a test a 20 V signal was fed from the aerial into the first stage of the receiver, a radio frequency amplifier. This signal is then passed through several stages of the receiver to eventually appear at the input to the AM detector. For the AM detector to work satisfactory it requires a minimum signal level of -3dB(mW). Calculate the required minimum gain of the fifth intermediate amplifier given the data in TABLE 1.

Stage Gain

RF amplifier +10 dB

Mixer -7 dB

BPF -1 dB

IF1 +15 dB

IF2 +15 dB

IF3 +20 dB

IF4 +10 dB

TABLE 1

20 V

(75 )

FIG. 1

2. As a rule of thumb, the perceived noise from a source falls by 6 dBA with every doubling of the distance from the source.

If a 1 MW wind turbine (FIGURE 2) produces 103 dBA of noise within one metre of its base, estimate the distance from the turbine at which the noise can be reckoned to have fallen below the background noise level of 40 dBA.

Background level

Distance

FIG. 2

3. A simplified model of ADC noise refers the noise to a noisy input source resistance Rn while assuming the rest of the signal path to be noiseless.

FIGURE 3 represents a particular 18-bit ADC that has a 10 V input

voltage range. The ADC has a bandwidth of 1 MHz.

Calculate the maximum value of Rn if the resolution of the ADC is not to be adversely affected by thermal noise. Assume the ADC operates at 25°C.

[N.b. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values possible on its output.]

Analogue input

Rn

1

Digital output 18 lines

18

FIG. 3

4. The specification for a 4-way TV antenna amplifier [FIGURE 4] is given

in TABLE 2, below.

TABLE 2

FIG. 4

(a) Determine the voltage required on the input of the amplifier to give the maximum output of 85 dBV.

(b) If the signal level from the aerial is 5 dBmV and the input noise level is 20 dBV, calculate the signal-to-noise ratio on the output of the amplifier.

5. A voltage amplifier ideally should have the input-output relationship of

vo = 100vi but in practice the relationship is vo = vi(98 + 2vi).

Calculate the %age second harmonic distortion present in the amplifier's output for a sinusoidal input of 10 mV r.m.s.

Note: Question 6 from the attachment is not addressed, as data is missing from previous questions.

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