Phys 312 - Assignment 8 - Due 1 April 99

1.

Fundamental constants from LED data. In class, we measured the threshold voltage to get appreciable light from various LED's (red, yellow, green, blue). Use these data to obtain a rough estimate of h/e, assuming that all the energy eV gained by an electron passing through the LED is transferred to a single photon. Plot (by hand) the data to check this simple assumption.

Wavelength	Frequency	Voltage
in nm	in 1014 Hz	in volts
660	4.54	1.35
630	4.76	1.46
590	5.08	1.58
565	5.31	1.66
450	6.66	2.28

2.

Circuit parameters. A general circuit is characterized by the three quantities R, C, L.

(a)

What are the dimensions of these quantities in the SI? Optional: what are their dimensions in the gaussian system (they are a lot simpler and more intuitive, but in this course we have agreed to use SI).

(b)

What are the dimensions of the product LC? What is its physical meaning?

(c)

What are the dimensions of the product RC? What is its physical meaning?

(d)

What are the dimensions of R/L? What is its physical meaning?

(e)

Form a dimensionless combination of R, C, L. What is its physical meaning?

3.

Passive low pass filter. As I mentioned in class, one stage of an archaic AM receiver consists of a low pass filter which removes the RF (radio frequency) carrier wave, leaving the AF (audio frequency) signal. The simplest passive filter (i.e., a filter which does not involve active elements such as transistors), consists of a resistor and a capacitor.

(a)

Sketch this filter

(b)

Show that

$$\left\vert {\frac{V_{{\rm out}}}{V_{{\rm in}}}}\right\vert ^{2}={\frac{1}{1+(\omega RC)^{2}}}.$$ (1)

Plot this transfer function and show that it has the right properties to function as a low pass filter.

(c)

Choose appropriate values of R and C for an AM receiver.

(d)

Our simple filter has a very slow "roll-off"; ideally, one would like a "brick wall" transfer function which is 1 up to some frequency $\omega _{0}$ and zero otherwise. Some improvement is obtained by incorporating an inductor into the filter, as discussed in class and sketched here.

(e)

Find the transfer function for this filter. Show that the response at low frequencies is the flattest when $R=\sqrt{2L/C}$. This can be done graphically by plotting the transfer function as a function of a dimensionless frequency for several values of a dimensionless parameter that is proportional to L. Note that for L=0 we are back to the previous case.

(f)

How does the transfer function behave at high frequencies?

4.

Using CMOS technology (with enhancement MOSFETS), as in Bloomfield, page 481, draw the circuit for an OR gate. Make four replicas of your drawing and indicate explicitly the voltage (or charge) on all the gates and nodes (you may just color the ones that are positive) for the four different possible inputs. Verify that the output is in agreement with the truth table for OR.