A three-stage amplifier is to have an overall noise temperature no greater than 70 K. The overall gain of the amplifier is to be at least 45 dB. The amplifier is to be built by adding a low-noise first stage to an existing two-stage amplifier that has the gains and noise figures shown below. (The stage numbers refer to locations in the new amplifier.) Noise Power Gain Figure Stage 3 dB 20 dB 6 dB 15 dB 3 (a) What is the minimum gain (in decibels) that the first stage can have? (b) Using the gain you calculated in part (a), calculate the maximum noise figure (in decibels) that the first stage can have. (c) Suppose the gain of the first stage could be increased by 3 dB without affecting its noise figure. What would be the effect on the noise temperature of the complete amplifier?