A receiver requires 10 nW as input power. If all the system losses add up to 50dB, then how much power is required from the source?
here, the power required by the receiver is the output power and that required from the source is input power.
Gain in dB=10 log(output power/input power)
we have, loss in dB = -gain in dB = 10 log(input power/output power)
or, 50 = 10 log(input power/10nW)
or, anti-log(5) = input power/10 nW
so the power required from the source is antilog(5)*10nW = 1 mW
Well, if the system losses add up to 50dB, it means they are practically hiding under a rock. Trust me, they're pretty good at disappearing! Now, back to the question at hand.
To find out how much power is required from the source, you need to apply some magical math. You see, dB is a logarithmic scale, so we'll have to take an unruly leap to reverse engineer this. Hang on tight!
First, let's convert the dB loss to a linear scale. Remember that dB = 10 * log10 (Power_out / Power_in). In this case, the ratio is the power loss, so 50dB = 10 * log10 (Power_loss).
Now, since the losses add up, we can subtract them from the input power to find the required power at the source.
But wait, there's more! Since we're dealing with power, not just any power but nano-watts, we'll have to do some power of 10 gymnastics. So, let's convert 10 nW to regular old Watts - that's 10 x 10^-9 W.
Finally, applying all the magic we've just learned, the required power from the source is equal to (Power_in / 10^(Loss/10)).
But hey, who needs all this complexity anyway? Let's just say the source needs a power supply big enough to light up a clown's nose at a circus – "Gigawatts of laughter!"
To calculate the power required from the source, we need to consider the system losses.
System losses are given in decibels (dB), which is a logarithmic scale. To convert dB to a linear scale, we use the following formula:
Linear scale value = 10^(dB/10)
In this case, the system losses add up to 50dB. So, the linear scale conversion would be:
Linear scale value = 10^(50/10) = 10^5 = 100,000
Now, let's calculate the power required from the source by considering system losses:
Power required from the source = Input power at the receiver / Linear scale value
Given that the receiver requires 10 nW (nanoWatts) as input power:
Power required from the source = 10 nW / 100,000
Power required from the source = 0.0001 nW
Therefore, the power required from the source is 0.0001 nW.
To determine the power required from the source, we need to subtract the system losses from the desired input power of the receiver.
1. Begin by converting the system losses from dB to power ratio.
- The conversion formula is: Power (ratio) = 10^(Loss (dB) / 10)
- In this case, the system losses are 50 dB.
- So, Power (ratio) = 10^(50 / 10)
2. Calculate the power ratio by evaluating the expression:
Power (ratio) = 10^(50 / 10) = 10^5 = 100,000
3. Now, subtract the power ratio of the system losses from the desired input power of the receiver.
- The input power required by the receiver is 10 nW (nanoWatts), which can be converted to Watts by dividing by 1 billion (1 nW = 1e-9 W).
- The power required from the source is: Power (source) = Power (receiver) / Power (ratio)
- In this case, Power (receiver) = 10 nW = 10e-9 W
4. Substitute the values into the equation:
Power (source) = (10e-9 W) / 100,000
5. Calculate the power required from the source:
Power (source) = 10e-9 W / 100,000 = 1e-14 W
Therefore, the power required from the source, considering a 50 dB system loss, is 1e-14 Watts.