Homework #1   Due 6pm wednesday, september 7th 
There may be updates to this homework, check back often!

1) You have a microphone which can be modeled as a sound-dependent
voltage source.  The peak voltage is 1mV, and the output resistance
is 10k ohms.
a) if you hooked a speaker up to the microphone directly, what real
impedance should the speaker have to maximize the power dissipated
in the speaker?  
i) What is the maximum power delivered to the speaker
in Watts and in dBm.  
ii)Verify this with hspice
iii) If the speaker has a real impedance of 8 ohms,
what is the maximum power delivered to the speaker in Watts and dBm?
b) due to high frequency noise, you want to put a low pass filter
with a single pole at 10kHz between the microphone and the speaker.  
i) can you do this by adding a single passive component, independent of
the
input resistance of the speaker?  If so, what is it, and what value
do you choose?
ii) if we assume that the speaker impedance varies between 1 and 100
ohms, design a single pole low pass filter to go between the microphone
and the speaker that does not degrade the maximimum power delivered 
to the speaker by more than 3dB.
iii) go to digikey.com and find the cheapest parts that will implement
your circuit.  What will your filter cost in quantities of 1000?
c) you put an amplifier between the microphone and the speaker
(assume that the low pass filter and the high frequency noise
are gone).  The amplifier has a voltage gain of 100, an input
impedance of 1M Ohm, and an output impedance of 8 Ohm.  If the
amplifier output is hooked up to an oscilloscope (not the speaker),
and the scope input impedance is 10M Ohm,
i) what is the voltage and power gain of the amplifier (in dB)?
If the amplifier is hooked up to an 8 Ohm speaker,
ii) what is the voltage and power gain of the amplifier (in dB)?
iii) what is the maximum power delivered to the speaker (in dBm)?
d) a different amplifier has a voltage gain of 1, and an output
impedance
of 0.1 Ohm, and we use the 8 Ohm speaker 
i) what is the voltage gain in dB,
ii) the maximum power delivered to the load (in dBm)?

2) You're designing a power-line communication system for home 
automation (like X-10) with signals at 100kHz.  You need a high-pass
filter to attenuate the 60Hz line voltage.
a) what pole frequency should you use to get
i) no more than 30% attenuation of the amplitude of the 100kHz signals?
ii) no more than 6 degrees of phase change on the 100kHz signals?
b) what attenuation of the 60Hz signal do you get in each case (in dB)?
c) implement both filters and verify using spice.

3) You are fixing an old radio, and need to design a channel tuner for
the FM band using an LC tank.  You're taking the signal straight out of 
the antenna (assume 75 ohms).
a) how much tuning range do you need in your passive components to
cover the FM band?
b) design your LC tank using parts from Digikey.  Estimate the voltage
gain (in dB).  Estimate the power gain (in dB).

4) You've finished your old radio, and discover that you can pick 
up stations that have signals as low as -80dBm.
i) How many Watts is that?
You put out 10 Watts with your home built speakers.
ii) How many dBW is that?  dBm?
iii) You tune in a station with a signal strength of -80dBm and
you crank the volume up to the max on your stereo.  What is the 
overall power gain from the input (RF) signals, to the output (audio)
signals (in dB)?

5) With simple arithmentic (and without using a calculator),
show what the power gain is for 6dB, 9dB, 13dB, 7dB, 4dB, 117dB, 116dB.