Pre-Work for Knowledge Integration 5 Spring 2017

(Due April 10, 2017)

Here is a list of pre-work questions for KI5. You are encouraged to discuss the content within your group and work through the questions as a group. Your group may be called during the KI discussion sessions on 4/11 and 4/12 in class. You are required to submit written answers individually to the questions using the dropbox in the BC-infill by 4pm on 4/10. Please write your name on every page of your answer sheets and start a new answer sheet for each question. There are a total of 7 questions and each question has a number of subquestions. 1. The receiver portion of a radio system is shown in Figure 1 in the green shaded

box. Using the knowledge you learned from the prior KI modules and from the junior level courses (ECE312/332/342), briefly describe the functions of each component in the receiver portion of a radio system in terms of how each component transforms the receiving signal from the antenna to the input of the A/D converter for further processing and storage.

Figure 1. The top-level block diagram of a radio system

2. Amplifiers are extensively used in the baseband portion of a radio receiver

system to condition the baseband signal to produce an output signal ready for digital sampling and storage. Some of the key design features of baseband amplifiers include

i. DC gain, ii. output swing,

iii. power consumption, and iv. bandwidth.

If you were to use a simple single-ended MOSFET common source amplifier for the baseband signal, consider the following design scenarios and choose the correct answer(s) for the required tradeoffs.

i. To increase DC gain of the amplifier, you would expect (circle all that apply)

a) Increase in power consumption b) Decrease in bandwidth c) Decrease in output swing d) All of the above

ii. For the choice(s) you made above, identify one component characteristics (RD, Ids, W, L, Vsat, Vdd, Vout_DC ) that you will use to increase DC gain and to cause changes in other specs.

iii. To increase bandwidth of the amplifier, you would expect (circle all that apply)

a) Increase in power consumption b) Decrease in DC gain c) Decrease in output swing d) All of the above

iv. For the choice(s) you made above, identify one component characteristics (RD, Ids, W, L, Vsat, Vdd, Vout_DC ) that you will use to increase bandwidth and to cause changes in other specs.

3. Oscillators are widely used in radio systems as carrier signals for up-conversion and down-conversion. A simple oscillator circuit can be implemented using an L-C circuit, assuming parasitic resistance within the LC loop is negligible.

i. Derive the transfer function of the simple LC oscillator and draw its pole locations.

ii. If parasitic resistance within the LC loop can’t be ignored, re-draw the pole locations

iii. What circuit technique can you provide to tackle the impact of parasitic resistance in the LC loop? Draw a circuit schematic to show your idea.

4. Consider the op-amp circuit shown in Figure 2, which connects two impedances

Zf and Zi in a closed-loop inverting-amplifier configuration:

Zi

Zf

-+

Vi Vo

Figure 2. General Inverting Amplifier Configuration

You may assume the op-amp has very large input-impedance, so that essentially zero current flows into the op-amp (+,-) inputs. The operational amplifier provides an open-loop gain as (here V+ and V- denote the input terminal voltages):

( )( )oV A s V V

Calculate the closed-loop transfer function (from Vi to Vo) of this circuit for the following two cases (for A(s)):

i. For an ideal op-amp you may assume a constant open-loop gain: ( )A s A

You may also assume that this gain is very large, and hence to a very good

approximation o

i

V

V should be independent of A.

ii. For a non-ideal op-amp assume an open-loop transfer function of the form:

( )1

AA s

sT

You may assume that the DC gain A is very large, and hence to a good

approximation o

i

V

V should look like the answer from part i multiplied by a

first-order transfer function.

5. Now consider the circuit shown in Figure 3, and note that this is a special case of the circuit you analyzed in question 4.

-+

Vi Vo

Ri

C

Rf

Figure 3. Simple Filter Circuit

i. Use the results from question 4 to calculate the closed-loop transfer function (from Vi to Vo) of this circuit for the following two cases: a) Ideal op-amp assumption (open loop gain A). b) Non-ideal op-amp assumption (open loop gain A(s)).

ii. Consider the following values for the components: 10 , 1 , 100f iR k R k C nF

Calculate the Bode plot (using Matlab) for this filter in the ideal op-amp case (A(s)=A). Answer the following (compare the theoretical answers to the Matlab Bode plot): a) What kind of filter is it? b) Where is the break frequency? c) What is the closed-loop DC gain?

iii. Consider the non-ideal op amp case and assume the following op-amp parameters for A(s):

410 , 0.1secA T

Repeat the analysis from part ii and compare the results. Consider also the

open-loop rolloff pole at 1

sT

and answer the following (again compare

theoretical answers to Bode plot). a) What is the break frequency for the open-loop op-amp pole? b) What is the break frequency for this pole in the closed-loop circuit?

iv. Is the low frequency roll-off pole in the non-ideal op-amp (transfer function A(s)) a major issue for the closed-loop circuit (explain)?

v. Why do we need such a large open loop gain for the op-amp (e.g., 104 or higher) when the closed loop circuit only implements a modest gain (e.g., 10)?

vi. This circuit implements a generic first order transfer function. Could you cascade these circuits to build any (higher order) transfer function (explain)?

6. Repeat the analysis from question 5 for the circuit shown in Figure 4 below

(note this is again a special case of the circuit you analyzed in question 4):

-+

Vi Vo

R1

C2

R2

C1

Figure 4. Alternative Filter Circuit

For the component values assume the following:

1 2 1 21 , 10 , 10 , 100R k R k C F C nF

For the op-amp parameters assume the same values as in question 5. 7. Figure 5 depicts the receiver board from Silicon Lab.

In the schematic different parts of the circuit can be distinguished. The RF circuit and matching network A printed balun that plays the role to equalize the signals in both branches of

the antenna The antenna built in the multi plane PCB with vias that generates the 3D

structure shown in the lower scheme A PCB transmission line that connects the RF circuit with the antenna

Figure 5. Receiver board from Silicon Lab

With this information in Figure 5, answer the following questions:

i. What is the function of the matching network? (Hint: Think in terms of circuit theory, assuming that the antenna is the load to the RF circuit)

ii. Assume that the PCB material has a relative permittivity of 4.4 and a thickness of 1.55mm. The circuit operates at 433 MHz. Do the dimensions of the antenna and transmission line conform to the wavelength? Explain.

iii. The RF circuit and the antenna are connected through a transmission line printed in the circuit board. What is the approximate impedance of the transmission line using the dimensions of the transmission line shown in Figure 6 below?

a) The approximate value is 50 Ω b) The approximate value is 75Ω c) The approximate value is 90Ω d) The approximate value is 120Ω e) None of the above

iv. The arrows in Figure 5 indicate the direction of maximum radiation power. Based on the antenna layout, can you justify this pattern with simple concepts?

Video Presentation for Knowledge Integration 5 Spring 2017

(Due 5pm, April 15, 2017)

Video presentation is a part of the KI exercise where you use the KI5 content you learned to make a short 7-minute video online. The details of KI5 content is given in the separate pre-work assignment. The video presentation should include the following:

1. Introduction of the signal receiving circuit of a radio system. 2. Specific key concepts in each of the junior year courses (ECE312, ECE332, and ECE342) that are

used in building the receiver circuit in a radio system. 3. A summary of how specific key concepts are integrated in building the receiver circuit in a radio

system.

You can record the video presentation at your own time using the recommended web tool(s). You must upload the final version of the presentation no later than 5pm on 4/15 (Saturday). Your video presentation will be judged by a small group of your peer students using a scoring rubric.

A few tips for making the video presentation:

1. Introduce yourself first. 2. Look into the camera when you speak. 3. Speak clearly and avoid using complex sentences and phrases. 4. Accompanying slides can help you make your point, but keep the slides simple and easy to read. 5. Be concise and don’t get into too much detail, and keep it within the 7 minute time limit.