Transmission Line Power Loss Calculations

[Paymemoney]

Homework Statement

A 3kW radio signal generator is connected via a transmission line having an attenuation of 0.4 dB/m.
Generator and load impedance are matched to the line.
i) How long may the line be, if the load must receive at least 1kW of power?
ii) How much power is dissipated by the 7th metre of line?

Homework Equations

GAIN=10log(Pout/Pin)

P=vi=v$$\hat{}$$2 / Z = i$$\hat{}$$2 * Z

A = 32.5$$/$$20log10F $$/$$ 20log10 D

The Attempt at a Solution

i)I used the GAIN formula to determine the power out and then i used the P=v^2/Z to find the impedance.
Line is 2.7x10^-6 long.

And i don't think this is correct, because i don't have any voltage value to input in the P=v^2/Z formula.

ii)I used the P=v^2/Z to find the power dissipated by the 7th meter of line.

the answer is 38.5x10^-9

Could someone tell me if this is correct.

 

[Redbelly98]

Welcome to Physics Forums

The 2.7x10^-6 m figure is wrong. But, maybe thinking about the following question can help get you started in the right direction:

For 1 meter of line, and the given attenuation of 0.4 dB/m, how much power would there be (Pout=___?) for 1 m of line?​

 

[Paymemoney]

Welcome to Physics Forums

The 2.7x10^-6 m figure is wrong. But, maybe thinking about the following question can help get you started in the right direction:

For 1 meter of line, and the given attenuation of 0.4 dB/m, how much power would there be (Pout=___?) for 1 m of line?​

Thanks I'm glad to be here.

Well this is what the result will be if the Pin=3kw & GAIN=0.4dB/m
So by using the GAIN formula i get the result:

Pout=3289.43W.

 

[Born2bwire]

How can the power increase over a line of attenuation?

 

[Redbelly98]

Good point. The transmission line causes attenuation, not gain.

 

[Paymemoney]

ok, well this is how i worked it out.

GAIN=10log(Pout/Pin

0.4=10log((Pout/3*10^3)

0.04=log(Pout/3*10^3)

10^0.04=(Pout/3*10^3)

Pout=(10^0.04)*(3*10^3)

Pout=3289.43W

Have i done something wrong, coz i can't see anything wrong.

 

[Redbelly98]

Pout=3289.43W

Have i done something wrong, coz i can't see anything wrong.

Something is wrong, since the power out should be less than the 3 kW input. That is the meaning of the word attenuation.

Since the transmission line causes loss of power, -0.4 dB should be used for the gain.

 

[Paymemoney]

Something is wrong, since the power out should be less than the 3 kW input. That is the meaning of the word attenuation.

Since the transmission line causes loss of power, -0.4 dB should be used for the gain.

oh, now i know where it was wrong silly me -_-.

 

[Paymemoney]

Well after doing it again i got Pout=2736.03W.

 

[Redbelly98]

Okay, that's right.

Next, how many dB would give Pout = 1000W?

 

[Paymemoney]

ok, by using the GAIN formula:

GAIN=10log(1000W/3000W)
GAIN=-4.77dB/m

 

[Redbelly98]

Okay, though the units are actually -4.77 dB (no "/m") in this calculation.

Now to answer the question. How many meters of cable would give that -4.77 dB?

 

[Paymemoney]

could you tell me what formula to use?

 

[Redbelly98]

At this point you don't need a formula to plug the numbers into. You'll need to think about what the numbers actually mean.

Use the information in the problem statement, and the fact that you have 4.77 dB of attenuation.

Good luck!

 

[Paymemoney]

thanks for the help, i think i get what you mean after thinking about it. If i came across anymore problems i will post them.

so just to clarify, 4.77db would give you appox 11.9m. In ii) the power dissipated would be the amount of power dissipated from 1m times 7m which would give you the power dissipated for the 7th meter of line.

 

[Redbelly98]

thanks for the help, i think i get what you mean after thinking about it. If i came across anymore problems i will post them.

so just to clarify, 4.77db would give you appox 11.9m.

Yes, I agree.

In ii) the power dissipated would be the amount of power dissipated from 1m times 7m which would give you the power dissipated for the 7th meter of line.

Your description doesn't make sense to me. The way I interpret the question is as follows:

How much power is dissipated in the 7th meter, i.e. between x=6m and x=7m?
To answer that, you'll need to calculate the power (think of it as Pout) at x=6m and at x=7m, given the 3000W Pin and the -0.4 dB/m power loss.
From that you can figure out how much of the power was lost in that 7th meter.

 

[Paymemoney]

Yes, I agree.


Your description doesn't make sense to me. The way I interpret the question is as follows:

How much power is dissipated in the 7th meter, i.e. between x=6m and x=7m?
To answer that, you'll need to calculate the power (think of it as Pout) at x=6m and at x=7m, given the 3000W Pin and the -0.4 dB/m power loss.
From that you can figure out how much of the power was lost in that 7th meter.

so, basically the value i found out from before of 2736.03W would then be multiplied by 7 to get the power lost in the 7 meters.

 

[Redbelly98]

so, basically the value i found out from before of 2736.03W would then be multiplied by 7 to get the power lost in the 7 meters.

...giving you 19kW lost. Which is quite impossible, given that there were only 3kW to begin with.

 

[Paymemoney]

ok, i made Pin=3000W & GAIN=-2.8dB
From that i calculated the Pout as 1574.42W. So therefore the power loss from 7 meters of line is 1574.42W.