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MECH 372 / ENGR 372
Space Systems Design and Engineering II
 
Assignment #2 - Introduction to Electronics - SOLUTIONS
 
 
Objective: The objective of this assignment is to demonstrate an understanding of the basic electronic concepts, components and their functions. 

PASSIVE COMPONENTS

1. A voltage divider with 2 resistors has a 5 kilo-ohm resistor "on top" and a 10 kilo-ohm resistor "on bottom".  The supply voltage is 10V.  

  1. What is the output voltage?

Vout = Vin*Rb/(Rt+Rb) = 6.7V

  1. How much current flows through the top resistor?

It = Vt/Rt=3.3V/5k-ohm = 0.667 mA

  1. How much current flows through the bottom resistor?

Ib = It = 0.667mA

  1. How much power is dissipated in the top resistor?

Pt = Vt*It = 2.2 mW

 

2.  Two inductors are wired in parallel.  One has a value of 50 microHenries and the other has a value of 20 microHenries.  What is the overall equivalent inductance of the parallel circuit?

1 / (1/50 + 1/20) = 1 / (.07) = 14.29 microHenries

 

3.  Why are capacitors often found between the power bus supply line and the ground line?

They act as low-pass filters (given the inherent levels of resistance found in the circuit and its wiring), filtering out the ripple (high frequency) and transients in the supply line.

 

4. Refer to Slide 13 from the Introduction to Electronics Slide package.  This shows the voltage response of an RC circuit as drawn.  If the capacitor starts in a discharged state such that Vc = 0V and then you close the switch, the voltage value of Vc grows exponentially as shown, until it reaches the value of the input voltage Vb (which is 1 volt for the example in the slide).  The speed of growth depends on the values of R and C.  One way to exploit this feature is to use this as the basis of a timer.  When you want to start timing, you close the switch.  Then you use a circuit like a comparator on Slide 23 to compare Vc with a reference voltage; the reference voltage might be created by a voltage divider as shown on Slide 11.  For example, you might have a reference voltage that is ~0.63*Vb, which means that Vc would surpass that point after one time constant.  One time constant is R*C seconds.

a) OK, given all of that, let's assume we want to build exactly this type of timer such that it hits its timer value at a time of R*C (believe it or not, the units of ohms * farads = seconds).  Let's assume you want to set the timer for 5 sec and you are using a Capacitor of 100 microFarads. What value of a resistor R should you select?

     RC=5 sec, so R = 5/C = 5/.0001 = 50 kohms

b) OK, now you're going to use the same circuit as a low-pass filter such as that shown on Slide 14.  Now, you want to select a new resistor R such that the RC circuit passes signals with a frequency less than 100 rad/sec but filters out frequencies above this level.  100 rad/sec would be considered to be the "cutoff frequency." Assuming you are stuck with the same 100 microFarad capacitor but that you can choose any Resistor value, what value should you select for the resistor?

     1/RC = 100 rad/sec, so R = 1/(100 rad/sec * 100 microFarads) = 100 ohms.

c) Slide 14 shows the frequency response of the RC circuit pictured on Slide 13.  If you switch the locations of the resistor and capacitor in that circuit, the circuit becomes a "high pass filter" instead of a "low pass filter." The cutoff frequency is still 1/RC, but now this is the frequency below which signals are attenuated and above which are passed with little to no attenuation.  Estimate what you think the resulting Amplitude Response for this filter would be with a simple sketch.  The Amplitude Response is the top portion of the graph shown on Slide 14.  A hand sketch is fine, but be sure to draw it approximately to scale, and label the axes.

Estimated Amplitude Response

  

5. The RLC circuit shown below has a transfer function of Vo/Vi = (s) / (Ls2 +  Rs + 1/C).  For this problem, assume that L=R=1 and C=1/400. 

Use Simulink to create a simple model of this system using the transfer function block - see below.  Use a sine wave for the input, and use a scope to show a dual plot of both the input as well as the output of the transfer function.  The snapshot of your model might look something like this (you need to figure out what the transfer function is):

 

  1. Use your simulation model to plot the filter's time response to a sine wave with frequency 1 rad/sec, a sine wave with frequency 20 rad/sec, and a sine wave with frequency of 100 rad/sec (assume a magnitude of 1 for all inputs).   Show the dual scope output for each case, and comment on how the filter affects the magnitude and the phase of the signal.  Note - if your Simulink time responses don't look as smooth as they should be (given that these signals are sine waves), try going to Simulation - Configuration Parameters via the menus and changing the "Max step size"; for example, you might try 1e-4.  Also, you might want to change the duration of your simulation from the default of 10 sec to something more appropriate - you want to show numerous cycles.  Also, make sure your simulation runs long enough that you have reached steady state.

For w=1 rad/sec:

For w=20 rad/sec:

For w=100 rad/sec:

Comment on the results in terms of the filter's affect on amplitude and phase.

The magnitude is dramatically reduced at w=1 rad/sec and w=100 rad/sec; however, it is unaffected at w=20 rad/sec.  At w=20 rad/sec, there is no phase shift, but there is a phase shift for the other two input frequencies.

  1. Use Matlab to generate a frequency response (Bode plot) of the filter.  What information does a Bode plot provide? How does your Bode plot compare with the outputs from the part a?

The Bode plot shows the response of a sinusoidal signal as it is transformed from input to output and is used to characterize linear systems.  It shows how the sine wave's magnitude and phase varies as a function of the frequency of the wave.  The plot matches what we saw from (b) in terms of magnitude and phase.

MATLAB Code:

>> num=[1 0];
>> den=[1 1 400];
>> sys=tf(num,den);
>> bode(sys);grid

  1. Explain why this circuit is called a bandpass filter.

It is called a "bandpass" filter since it effectively allows frequencies within a certain frequency band to be passed through the system at full (or close to full) magnitude; for frequencies far enough above and below the passband, the wave is severely attenuated.

  1. The R, L, and C values used for this problem were selected for simplicity.  These are not typical values for these components for most applications.  For normal applications, would you expect the values to be higher or lower for resistors, capacitors, and inductors (the answers may differ for each type of component).
Resistors - normally much higher by several orders of magnitude
Capacitors - normally much lower by several orders of magnitude
Inductors - normally much lower by several orders of magnitude

   

EXAMPLE CIRCUIT

6. The figure below shows the schematic of a simple thermostat circuit.  The purpose of this problem is to understand the functions that each portion of the circuit plays - you are not being asked to perform any quantitative circuit analysis.  Thermostats are common in spacecraft; in addition, this circuit demonstrates a nice level of functional decomposition that is also common in spacecraft.

RT is a thermister (a resistor whose resistance depends on temperature - it is the sensor or transducer in this problem), and  V+ is the supply voltage; the values of the other resisters are unimportant to answering the questions below.

For those of you unfamiliar with the functionality of a basic thermostat, the temperature is compared with some reference (a temperature set-point, or a quantity representing one).  If the temperature falls below the reference, then a control signal causes a heater to be turned on.  

By looking at the circuit, match each portion of the circuit - A through E - with one of the stated functional roles listed here:

- low-pass filter - smooths out the voltage from the sensing circuit to get rid of high frequency noise
- transistor switch - when input is high, this switches on current to heater
- reference circuit - voltage divider sets a voltage representing the temperature setpoint
- sensing circuit - converts change in thermistor resistance to a voltage representing temperature
- comparator - compares temperature with setpoint and goes high to turn on heater when temp is low
A: sensing circuit - converts change in thermistor resistance to a voltage representing temperature
B: reference circuit - voltage divider sets a voltage representing the temperature setpoint
C: low-pass filter - smooths out the voltage from the sensing circuit to get rid of high frequency noise
D: comparator - compares temperature with setpoint and goes high to turn on heater when temp is low
E: transistor switch - when input is high, this switches on current to heater

 

ANALOG & DIGITAL CIRCUITRY

7. Short Answer & Computation

a) Give an example of a value in the world that is continuous and would naturally be represented by an analog voltage. Temperature is one of many possible answers.

b) Give an example of a value in the world that is binary and would naturally be represented by a discrete voltage levels. The state of a switch is one of many possible answers.

c) Convert the decimal number 22 into a standard binary representation, a standard octal representation, and also a standard hex representation: binary = 10110, octal= 26, hex = 16

d) Convert the standard binary number 01010101 into a decimal number: 85

  

8. The digital circuit below is an example of an encoder.  This particular encoder is often used when there is an assumption that one and only one of 4 binary input lines reads 1 (with the rest reading 0).  Given this, the encoder outputs two bits that together represent a single binary number.

  1. Generate the truth table for this circuit by filling in the Truth Table provided.
A3 A2 A1 A0 F1 F0
0 0 0 1 0 0
0 0 1 0 0 1
0 1 0 0 1 0
1 0 0 0 1 1
  1. Complete the sentence describing the functionality of this circuit: Given a single HIGH input line, this circuit will output a 2-bit number that represents _the number of the HIGH input line____________________________.

  c. In doing this problem, we assumed that one and only one line was high at any given time.  What would happen if no lines were high or if more than one line was high at the same time?  What could be done with respect to the design of the circuit to explicitly address such a possibility?

     Undetermined behavior, which could be a disaster. 

     In the design of the circuit, you could explicitly add truth table lines for each such situation and then map it so the exact output case that is appropriate.  Sometimes this is done with an extra "error" output line that gets set high if such conditions are experienced.

 

 

COMPUTERS / MICROCONTROLLERS

9. Short Answer

a) A "Controller" consists of 3 very specific components along with a bunch of miscellaneous components.  What are the 3 main components of a controller?  A processor, memory, and i/o.

b) It is quite possible to "compute" using a variety of technical approaches, such as using analog circuits (a.k.a. analog computers built from op-amps circuits, which can add, subtract, multiple, divide, integrate, etc.), digital circuitry (from which you can build complex state machines and reasoning systems), and of course computers.  Non-computer approaches like analog circuits and digital state machines are generally MUCH faster, less power, smaller, and so on.  Given this, what is the primary rationale for using full-blown computers when simpler computational approaches can meet desired computing tasks.  I'm looking for one very specific benefit/advantage of using conventional computers - This point was made several times during the lecture.  The flexibility of software

c) For each of the following computing acronyms, define the acronym and provide a simple 1-2 sentence description of what it is and does:

i. SPI: Serial Peripheral Interface - a Motorola standard for a full duplex synchronous serial data link allowing using a master/slave communications protocol and allowing multiple slave devices.

ii. I2C: Inter-Integrated Circuit - a Philips specification for multi-master serial communications using 2 bi-directional lines and typically used for "low-speed" communications.

iii. EEPROM: Electrically Erasable Programmable Read Only Memory - non-volatile memory, used to store small amounts of data.

iv. ALU: Arithmetic Logic Unit - fundamental component of a CPU that performs mathematical and logic operations

v. RAM: Random Access Memory - volatile memory for storing data with the ability to directly access data at any point (vs sequential storage, like a tape drive for which you need to cycle through data to the point you want)