EE 2212

PROBLEM SET 2

S. G. Burns

Due: Monday, 4 October

Note 1: Again, a reminder that some of the WEB browsers such as Firefox and shareware versions of Internet Explorer and Chrome and its derivatives may not display or print SYMBOL and ADOBE fonts correctly. There are also some issues with iOS. Also, shareware versions of WORD and WORD without the embedded symbol font may also have issues in this regard. For example, 1 kW should show as k followed by Greek upper case omega. If it displays or prints as 1 kW you have an issue with all Greek symbols! This could lead to errors with units since micro ”μ” will read as “m” and so forth which yields an error of 10⁹!!! Be careful.

Note 2: Unless otherwise stated, assume all operational amplifiers are ideal. Therefore you must use the summing point constraints as introduced in class to significantly minimize algebraic complexity.

Note 3: Includes some of my best humor stock!!!

1. Cascaded amplifier problems. Essentially, “plug and chug”. Figures P12.3, P12.5, P12.6, P12.9, 12.14, and P12.17 (pages 759 and 760) are cascaded operational amplifier circuits. Compute the voltage gain, = v_O/v_I for each circuit. Believe it or not, when you use summing point constraints and the circuit topologies we discussed in class, the voltage gain computation for each circuit can be done in ONE line! Also for added practice, compute the voltage gain in dB for each of these six circuits.

2. Non-linear feedback elements are quite common as we will observe later this semester. The non-linear circuit in the feedback network shown is called an analog multiplier. The terminal characteristics of the analog multiplier are defined as shown in the figure.

Show that this circuit can be used an analog signal divider. That is derive Vo in terms of

Vs1 and Vs2.

3. Active Analog Filter Topologies

You already know from our class discussions that Circuit 1 is an active analog Low-Pass Filter For each of the remaining three circuits, state whether the circuit will function as a low-pass or high-pass filter. Each of your answers must be accompanied by a brief explanation and justification incorporating the frequency dependent characteristics of the reactive circuit elements. That is you should look at the asymptotic impedance of the L and C if the input signal the frequency is very low or very high. Sketch the expected Bode plot for 20 log(Vo/Vs) as a function of log (f) labeling the corner frequencies. No equations are required!

4. Use a six-input summing amplifier design approach for this design. Since I have been taking guitar lessons (also violin by the way) through the UMD Fine arts Academy (I am not very good which means I should practice more). Design the electronic preamplifier for an electric guitar.

MCj04079760000[1]

There are six strings on an electric guitar and their frequency and musical note relationships are shown in the table. Each of the “humbucker” magnetic pickups for the six strings will be modeled as six signal sources v₁(t), v₂(t), v₃(t), v₄(t), v₅(t), and v₆(t).

DESIGN an operational amplifier system (guitar preamp/audio equalizer ) such that the resultant output, which you would listen to as the sum, meets the individual string amplitude specifications given in the last row of the table. .

Again, assume an ideal operational amplifier which allows you to use summing point constraints, however resistor values must be compatible with a mA 741, that is all resistors larger than 2kW. Your design must include a detailed, well-labeled circuit diagram showing six inputs; one for each string’s “humbucker” magnetic pickup transducer.

String 1 High E	String 2 B	String 3 G	String 4 D	String 5 A	String 6 Low E
v₁(t)	v₂(t)	v₃(t)	v₄(t)	v₅(t)	v₆(t)
f_{1 >}	f_{2 >}	f_{3 >}	f_{4 >}	f_{5 >}	f₆
12 dB	20 dB	-6 dB	6 dB	20 dB	30 dB Nice bass boost