Electrical Engineering Crossword (Issue 279)

The answers to Circuit Cellar’s October electronics engineering crossword puzzle are now available.

279-crossword-key

Across

1.    ERASABLE—The second “E” in EEPROM
4.    NYCRESISTOR—Brooklyn, NY-based open-community workspace [two words]
5.    WHITEHAT—A hacker with ethics may don one of these [two words]
6.    WIMAX—aka, IEEE 802.16
8.    STRUCTUREDQUERY—A type of data-management language [two words]
9.    PACKETSWITCHING—Data grouping method [two words]
11.    VOLTOHMMETER—Capable of measuring  voltage, current, and resistance [three words]
12.    ELUA—It’s free, open source, and embedded
13.    BUCK—A switched-mode power supply converter
14.    GOODPUT—This can be calculated by dividing a transmitted file’s size by the amount of time it takes to transfer the file
16.    GRAYCODE—One bit makes a difference [two words]
17.    UBUNTU—Linux-based OS
18.    WEARLEVELING—When applied to a flash memory, this technique can level out the amount of writes to any given memory block across the entire memory chip [two words]
19.    MOODLE—E-learning software developed by Australian computer scientist Martin Dougiamas
20.    CROSSEDFIELD—This type of microwave amplifier can also be used as an oscillator [two words]

Down

2.    LONGTERMEVOLUTION—Wireless communication standard [three words]
3.    CHEMILUMINESCENCE—A chemical reaction that creates a light emission
7.    BAXANDALL—A negative-feedback circuit used in high-quality audio amplifiers
10.    MICROKERNEL—µK
15.    PAUSEUS—BASIC command that creates a microsecond-based delay

 

Laurent Haas Wins the CC Code Challenge (Week 18)

We have a winner of last week’s CC Weekly Code Challenge, sponsored by IAR Systems! We posted a code snippet with an error and challenged the engineering community to find the mistake!

Congratulations to Laurent Haas of Paris, France for winning the CC Weekly Code Challenge for Week 18! Laurent will receive an IAR Kickstart: KSK-LPC4088-JL.

Laurent’s correct answer was randomly selected from the pool of responses that correctly identified an error in the code. Laurent answered:

Line 19 : Should be “write(*,*) average”

2013_code_challenge_18_answer

You can see the complete list of weekly winners and code challenges here.

What is the CC Weekly Code Challenge?
Each week, Circuit Cellar’s technical editors purposely insert an error in a snippet of code. It could be a semantic error, a syntax error, a design error, a spelling error, or another bug the editors slip in. You are challenged to find the error.Once the submission deadline passes, Circuit Cellar will randomly select one winner from the group of respondents who submit the correct answer.

Inspired? Want to try this week’s challenge? Get started!

Submission Deadline: The deadline for each week’s challenge is Sunday, 12 PM EST. Refer to the Rules, Terms & Conditions for information about eligibility and prizes.

Carol Willing Wins the CC Code Challenge (Week 17)

We have a winner of last week’s CC Weekly Code Challenge, sponsored by IAR Systems! We posted a code snippet with an error and challenged the engineering community to find the mistake!

Congratulations to Carol Willing of Encinitas, California, USA for winning the CC Weekly Code Challenge for Week 17! Carol will receive an Elektor 2012 & 2011 Archive DVD.

Carol’s correct answer was randomly selected from the pool of responses that correctly identified an error in the code. Carol answered:

Line 6: cons will incorrectly create a list of lists; use append instead for correct recursive reversal of list

2013_code_challenge_17_answer

You can see the complete list of weekly winners and code challenges here.

What is the CC Weekly Code Challenge?
Each week, Circuit Cellar’s technical editors purposely insert an error in a snippet of code. It could be a semantic error, a syntax error, a design error, a spelling error, or another bug the editors slip in. You are challenged to find the error.Once the submission deadline passes, Circuit Cellar will randomly select one winner from the group of respondents who submit the correct answer.

Inspired? Want to try this week’s challenge? Get started!

Submission Deadline: The deadline for each week’s challenge is Sunday, 12 PM EST. Refer to the Rules, Terms & Conditions for information about eligibility and prizes.

William McNamara Wins the CC Code Challenge (Week 16)

We have a winner of last week’s CC Weekly Code Challenge, sponsored by IAR Systems! We posted a code snippet with an error and challenged the engineering community to find the mistake!

Congratulations to William McNamara of The Colony, Texas, USA for winning the CC Weekly Code Challenge for Week 16! William will receive a CC T-Shirt and one year digital subscription/renewal.

William’s correct answer was randomly selected from the pool of responses that correctly identified an error in the code. William answered:

Line 5: the “do” needs to be on a separate line or have a semicolon in front of it.

2013_code_challenge_16_answer

You can see the complete list of weekly winners and code challenges here.

What is the CC Weekly Code Challenge?
Each week, Circuit Cellar’s technical editors purposely insert an error in a snippet of code. It could be a semantic error, a syntax error, a design error, a spelling error, or another bug the editors slip in. You are challenged to find the error.Once the submission deadline passes, Circuit Cellar will randomly select one winner from the group of respondents who submit the correct answer.

Inspired? Want to try this week’s challenge? Get started!

Submission Deadline: The deadline for each week’s challenge is Sunday, 12 PM EST. Refer to the Rules, Terms & Conditions for information about eligibility and prizes.

Issue 278: EQ Answers

Problem 1—Tom, an FPGA designer, is helping out on a system that handles standard-definition digital video at 27 MHz and stores it into an SDRAM that runs at 200 MHz. He discovered the following logic in the FPGA (see Figure 1).

Let’s see if we can work out what it does. To start with, what is the output of the XOR gate in?

Answer 1—When the 27-MHz clock goes from low to high, the first flip-flop changes state. Let’s say that its output goes from low to high as well. Then, when the clock goes from high to low, the second flip-flop’s output will become the same as the first.

On the clock’s next rising edge, the first flip-flop will change again, this time from high to low. And on the next falling edge, the second one will follow suit.

Putting it another way, following each rising edge of the clock, the two flip-flops are different. Following each falling edge, they’re the same. Since we’re feeding them into an XOR gate, the gate’s output will be high following the clock’s rising edge and low following the falling edge. In other words, the XOR gate’s is a replica of the clock signal itself!

Problem 2—Why is this necessary?

Answer 2—In many FPGA architectures, clock signals are automatically assigned to special clock routing resources, which are different from—and kept separate from—the routing resources used for “ordinary” signals. The tools actually discourage (or even prevent) you from using a clock as an input to a gate or to any input of a flip-flop other than the clock input.

Therefore, when you need to pass a clock into another timing domain as a signal, it becomes necessary to generate an ordinary signal that is a replica of the clock. This is one way to accomplish that.

Problem 3—What is the AND gate’s output?

Answer 3—The three flip-flops in the 200-MHz domain have a delayed versions of the (replica) 27-MHz clock signal. The first two function as a conventional synchronizer to minimize the effects of metastability. The third one, along with the AND gate, functions as an edge detector, generating a one-clock pulse in the 200-MHz clock domain following each rising edge of the 27-MHz clock. This pulse might be used, for example, to initiate a write request in the SDRAM for each video data word.

Problem 4—Tom decided to verify the circuit’s operation in his logic simulator, but immediately ran into a problem. What was the problem and what could be added to the circuit to make simulation possible?

Answer 4—There is a subtle problem here for a simulator: All of the flip-flops start out in the “unknown” state. Feeding that back (inverted) to the first flip-flop leaves it in an unknown state. The entire simulation will never get out of the unknown state, even though we can reason that it doesn’t matter which actual state the first flip-flop starts out in. The XOR gate’s output will be known after one full clock cycle. To fix this, it is necessary to explicitly reset the first flip-flop at the beginning of the simulation, then the rest of the circuit will simulate normally.

Jesper Poulsen Wins the CC Code Challenge (Week 15)

We have a winner of last week’s CC Weekly Code Challenge, sponsored by IAR Systems! We posted a code snippet with an error and challenged the engineering community to find the mistake!

Congratulations to Jesper Poulsen of København, Denmark for winning the CC Weekly Code Challenge for Week 15! Jesper will receive a CCGold Issues Archive.

Jesper’s correct answer was randomly selected from the pool of responses that correctly identified an error in the code. Jesper answered:

Line 23: Should be 0..@list-2 to avoid array overrun when taking $list[$i+1]

2013_code_challenge_15_answer

You can see the complete list of weekly winners and code challenges here.

What is the CC Weekly Code Challenge?
Each week, Circuit Cellar’s technical editors purposely insert an error in a snippet of code. It could be a semantic error, a syntax error, a design error, a spelling error, or another bug the editors slip in. You are challenged to find the error.Once the submission deadline passes, Circuit Cellar will randomly select one winner from the group of respondents who submit the correct answer.

Inspired? Want to try this week’s challenge? Get started!

Submission Deadline: The deadline for each week’s challenge is Sunday, 12 PM ESTRefer to the Rules, Terms & Conditions for information about eligibility and prizes.

Electrical Engineering Crossword (Issue 278)

The answers to Circuit Cellar’s September electronics engineering crossword puzzle are now available.

ACROSS

4.    ADIABATIC—Heat is neither gained nor lost
5.    DISCRETECIRCUIT—Made of resistors and transistors; not integrated [two words]
8.    FULLDUPLEX—Two-way communication [two words]
10.    KERMIT—Muppet-inspired protocol
12.    DEBIAN—Unix-like OS
14.    CHIRP—Conveys information
16.    FORTRAN—Others like it include BASIC and Pascal
18.    NANOKERNEL—Contains a minute amount of code capable of executing in the hardware’s privileged mode
19.    RHEOSTAT—Current regulator

DOWN

1.    BIPOLARJUNCTION—There are two types: NPN and PNP [two words]
2.    ECBBUS—1970s communication system for Zilog and Intel microprocessors [two words]
3.    VISUALSERVOING—Used to control a robot’s motions [two words]
4.    ATTOSECOND—10-18 of a second
6.    NICKELCADMIUM—This small, light, high-power type is commonly used in hand-held devices [two words]
7.    DEFCON—Place where hackers annually assemble
9.    PIGGYBACKING—Bi-directional data transmission
11.    GRASSHOPPER—Programming language for rhinos
13.    FLOSSMANUALS—Netherlands-based foundation that provides information about and access to free software [two words]
15.    RASPBERRYPI—An inexpensive SBC [two words]
17.    LIDAR—Laser-based measurement technique

 

Electrical Engineering Crossword (Issue 277)

The answers to Circuit Cellar’s August electronics engineering crossword puzzle are now available.

ACROSS

6.    ALGORITHM—Search engines use them to produce real-time results
9.    LOSSYCOMPRESSION—Condenses data by getting rid of some of it [two words]
11.    YOTTABYTE—Approximately 1,024 bytes
14.    PETAFLOP—Measures an FPU’s performance
15.    JQUERY—JavaScript library popularity contest winner
17.    THICKCLIENT—Able to function without a central server [two words]
18.    NYBBLE—4 bits
19.    DEGAUSSING—Gets rid of magnetism
20.    SPINTRONICS—aka, magnetoelectronics

DOWN

1.    YANG—Co-founded a multinational Internet company in 1994
2.    MICROSOFT—Originally created and sold BASIC computer programs for the Altair 8800 microcomputer
3.    CHARACTERLARGEOBJECT—Used to store large amounts of text [three words]
4.    ACGENERATOR—Changes mechanical energy into electrical energy [two words]
5.    DROPPER—Installs malicious code onto computers
7.    TRINITRON—Sony Corp.’s CRT technology
8.    BEAMWIDTH—Commonly specified at –6 dB, –10 dB, and –20 dB
10.    OVERCLOCKING—Makes the time go by more quickly
12.    FERROMAGNETIC—e.g., iron, cobalt, and nickel
13.    BAUDOTCODE—An early digital communication method [two words]
16.    AUTODYNE—Invented in 1914 by electrical engineer Edwin Armstrong, who is also credited with creating FM radio transmission

 

Issue 276: EQ Answers

Problem 1
Suppose you have an ordinary switch mode buck regulator. The input voltage is 100 V, the switch’s duty cycle is exactly 50%, and you measure the output voltage as 70 V. Is this converter operating in continuous conduction mode or discontinuous conduction mode? How can you tell?

Answer 1
If a switch mode buck converter is operating in continuous conduction mode, then the output voltage is the fraction of the input voltage as defined by the duty cycle. 100 V × 0.5 would equal 50 V. Therefore, this converter is operating in discontinuous conduction mode.

Note that continuous conduction mode includes the case in which synchronous (active) rectification is being used and the current through the coil is allowed to reverse direction when the output is lightly loaded. The output voltage in relation to the input voltage will still be defined by the switch duty cycle.

Therefore, we also know that the regulator in question is not using synchronous rectification, but rather is using a diode instead.

Problem 2
Since a diode can be placed in a High-Impedance state (reverse-biased) or a Low-Impedance state (forward-biased), they are sometimes used to switch AC signals, including audio and RF. What determines the magnitude of a signal that a diode can switch?

Answer 2
When diodes are used for signal switching, there are two considerations with regard to the magnitude of the signal relative to the DC control signal:

  • In the Blocking state, the reverse bias voltage must be greater than the peak signal voltage to prevent signal leakage. Also, a high-bias voltage reduces the parasitic capacitance through the diode. PIN diodes are often used for RF switching because of their ultra-low capacitance.
  • In the On state, the forward DC control current through diode must be greater than the peak AC signal current, and it must be large enough so that the current doesn’t approach the diode curve’s “knee” too closely, introducing distortion.

Obviously, the diode needs to be rated for both the peak reverse voltage and the peak forward current created by the combination of the control signal and the application signal.

Problem 3
What common function does the following truth table represent?

A B C X Y Z
0 0 0 ? 0 0 0
0 0 1 ? 0 0 1
0 1 0 ? 0 1 0
0 1 1 ? 0 0 1
1 0 0 ? 1 0 0
1 0 1 ? 0 0 1
1 1 0 ? 0 1 0
1 1 1 ? 0 0 1

Answer 3
The truth table implements a form of priority encoder:

Z is set if C is set, otherwise
Y is set if B is set, otherwise
X is set if A is set

In other words, C has the highest priority and A has the lowest. However, unlike conventional priority encoders that produce a binary output, this one produces a “one hot” encoding.

Problem 4
Write the equations for the logic that would implement the table.

Answer 4
The logic is quite straightforward:

Z = C
Y = B & !C
X = A & !B & !C

Electrical Engineering Crossword (Issue 276)

The answers to Circuit Cellar’s July electronics engineering crossword puzzle are now available.

Across
3.    CRAY—Seattle, WA-based supercomputer company founded in the 1970s
5.    SUPERSTATE—A subprogram common to several states [two words]
7.    ONESCOMPLIANT—Inverted bits’ value [two words]
11.    BACKPLANE—Lacks processing and storage
13.    FALSECLOCK—Locks on an incorrect frequency [two words]
15.    TERNARY—This signal is capable of taking on one of three conditions
16.    BLUMLEIN—Known for advancements in telecommunications and radar
17.    JABBER—XML messaging protocol (hint: prior to 2000)
18.    DIRECTCURRENT—Zero frequency [two words]
20.    SERIALTRANSFER—Moves data bit by bit [two words]

Down
1.    LYAPUNOV—Theory applies input-to-state (ISS) to systems with inputs
2.    LOWFREQUENCYOSCILLATOR—Produces a frequency below approximately 20 Hz [three words]
4.    HASHING—Security method
6.    SIGNIFICAND—aka, mantissa
8.    THYRISTOR—They have a four-layer N- and P-type construction
9.    HALFADDER—Combines two single binary digits [two words]
10.    DARKTRACE—A type of direct-view bistable storage tube [two words]
12.    FARADAYCAGE—Electric field-buffer [two words]
14.    SYMMETRIC—Uses the same key to code and decode
19.    KAHAN—Helped create the IEEE 754 floating-point computation specification

Electrical Engineer Crossword (Issue 275)

The answers to Circuit Cellar’s June electronics engineering crossword puzzle are now available.

Across

2.    UNIFIEDMODELING—Language that standardizes software specifications
3.    KELVINBRIDGE—Compares low resistance values [two words]
6.    THINCLIENT—A codependent program [two words]
10.    BANANAPLUG—Makes electrical connections [two words]
11.    CONDENSER—aka capacitor
13.    ASTABLE—A multivibrator circuit
15.    FLIPFLOP—A fundamental building block [two words]
18.    AMMETER—Used to calibrate current
19.    CLOCKGATING—Method of lowering dynamic power dissipation [two words]
20.    THERMIONICVALVE—Uses a vacuum to control electric current [two words]

Down

1.    VISITORPATTERN—Keeps an algorithm away from an object structure
4.    RUNTIME—Multi-lingual computer system
5.    FIELDEFFECT—This type is unipolar [two words]
7.    LISSAJOUSCURVE—An oscilloscope trace [two words]
8.    NONMASKABLE—Cannot be ignored
9.    CASCODECIRCUIT—Provides amplification [two words]
12.    CRON—Keeps things on schedule
14.    ROENTGEN—Radiation measurement
16.    RETFIE—Instruction that enables new interrupts to occur
17.    SELSYN—aka mag-slip

Issue 274: EQ Answers

The answers to the Circuit Cellar 274 Engineering Quotient are now available. The problems and answers are listed below.

Problem 1—What is wrong with the name “programmable unijunction transistor?”

Answer 1—Unlike the original unijunction transistor—which really does have just a single junction—the programmable unijunction transistor (PUT) is actually a four-layer device that has three junctions, much like a silicon-controlled rectifier (SCR).

 

Problem 2—Given a baseband channel with 3-kHz bandwidth and a 40-dB signal-to-noise ratio (SNR), what is the theoretical capacity of this channel in bits per second?

Answer 2—The impulse response of an ideal channel with exactly 3 kHz of bandwidth is a sinc (i.e., sin(x)/x) pulse in the time domain that has nulls that are 1/6,000 s apart. This means you could send a series of impulses through this channel at a 6,000 pulses per second rate. And, if you sampled at exactly the correct instants on the receiving end, you could recover the amplitudes of each of those pulses with no interference from the other pulses on either side of it.

However, a 40-dB signal-to-noise ratio implies that the noise power is 1/10,000 of the maximum signal power. In terms of distinguishing voltage or current levels, this means you can send at most sqrt(10,000) = 100 distinct levels through the channel before they start to overlap, making it impossible to separate one from another at the receiving end.

100 levels translates to log2100 = 6.64 binary bits of information. This means the total channel capacity is 3,9840 bits/s (i.e., 6,000 pulses/s × 6.64 bits/pulse).

This is the basis for the Shannon-Hartley channel capacity theorem.

 

Problem 3—In general, is it possible to determine whether a system is linear and time-invariant (LTI) by simply examining its input and output signals?

Answer 3—In general, given an input signal and an output signal, you might be able to definitively state that the system is not linear and time-invariant (LTI), but you’ll never be able to definitively state that it is, only that it might be.

The general technique is to use information in the input signal to see whether the output signal can be composed from the input features. Input signals (e.g., impulses and steps) are easist to analyze, but other signals can also be analyzed.

 

Problem 4—One particular system has this input signal:

Figure 1

The output is given by:

Figure 2

Is this system LTI?

Answer 4—In this example, the input is a rectangular pulse that can be analyzed as the superposition of two step functions that are separated in time, one positive-going and the other negative-going. This makes the analysis easy, since you can see the initial response to the first step function then determine whether the response following the second step is a linear combination of two copies of the first part of the response.

In this case, the response to the first step function at t = 0 is that the output starts rising linearly, also at t = 0. The second (negative) input step function occurs at t = 0.5, and if the system is LTI, you would expect the output to also change what it’s doing at that time. In fact, you would expect the output to level off at whatever value it had reached at that time, because the LTI response to the second step should be a negative-going linear ramp, which, when added to the original response, should cancel out.

However, this is not the output signal received, so this system is definitely not LTI.

Electrical Engineer Crossword (Issue 274)

The answers to Circuit Cellar’s May electronics engineering crossword puzzle are now available.Across

1.            MOSIPROTOCOL—Adds a state indicating ownership [two words]

3.            SPECTROMETER—Measures wavelengths

8.            SHELL—Protects an operating system’s kernel

10.          CHARGE—Q

12.          ASSIGN—A FORTRAN control statement

13.          HALL—American physicist (1855–1938) who had an “effect” [two words]

15.          FIELDPROGRAMMABLE—Configurable after purchase [two words]

17.          MOUNTPOINT—In a Linux system, create this first to access the queue [two words]

19.          CORDIC—Calculate digit by digit

20.          MEISSNEREFFECT—Flux jumping [two words]

 

Down

2.            INTERPROCESSCOMMUNICATION—Data exchanging method [two words]

4.            SQUIRRELCAGE—Commonly used in asynchronous motors [two words]

5.            DEGLITCHER—Type of delay circuit, serves as a pulse generator

6.            MERCURYARC—Emits  bright bluish-green light [two words]

7.            BALLGRIDARRAY—Packages ICs [three words]

9.            THREADEDCODE—A compiler technique [two words]

11.          DARAF—Unit of elastance

14.          AMPEREHOUR—3,600 coulombs [two words]

16.          RIPPLE—Unwanted undulation

18.          NIXIE—Used for numeric display

 

Electrical Engineer Crossword (Issue 273)

The answers to Circuit Cellar’s April electronics engineering crossword puzzle are now available.

Across

1.         BITDENSITY—Bits per inch of magnetic tape, for example [two words]

3.         KALMANFILTER—aka LQE [two words]

5.         EMBEDDEDSECURITY—Circuit Cellar columnist Patrick Schaumont covers this topic with articles about authentication, encryption, and electronic signatures [two words]

7.         HAMMING—Error-correcting code

8.         SPURIOUS—Unintentional

11.       LAND—Electronics and Computer Engineering professor at Cornell University and Circuit Cellar frequent contributor (many of his students contribute to Circuit Cellar as well)

13.       CLAPP—American inventor who developed an oscillator frequency standard

14.       ELECTRODE—Able to interact with nonmetallic circuit parts

16.       RINGOSCILLATOR—A feedback structure with an odd number of digital inverters [two words]

17.       PLESIOCHRONOUS—A system that’s not quite in synch

18.       OSCILLOGRAPH—Takes electric current measurements

19.       REFLECTEDBINARYCODE—Created by Bell Labs physicist and researcher Frank Gray [three words]

 

Down

2.         DEADBAND—Potentiometer’s part shortened by a tap [two words]

4.         BECHTOLSHEIM—Electronics engineer and co-founder of the company that created Java

6.         CHIPBIOMETRICS—Digital fingerprints [two words]

9.         INCANDESCENT—Illuminating

10.       ALOHANET—Computer networking system from the 1970s

12.       EEVBLOG—Where to find electronics engineer David L. Jones’s off-the-cuff online videos

15.       EULERMETHOD—Solves equations [two words]

17.       POPOV—Helped make electromagnetic radio waves more useful

Issue 272: EQ Answers

The answers to the Circuit Cellar 272 Engineering Quotient are now available. The problems and answers are listed below.

Problem 1—Why does the power dissipation of a Darlington transistor tend to be higher than that of a single bipolar transistor in switching applications?

Answer 1—In switching applications, a single transistor can saturate, resulting in a low VCE of 0.3 to 0.4 V. However, in a Darlington pair, the output transistor is prevented from saturating by the negative feedback provided by the driver transistor. If the collector voltage drops below the sum of the VBE of the output transistor (about 0.7 V) and the VCE(sat) of the driver transistor (about 0.3 V), the drive current to the output transistor is reduced, preventing it from going into saturation itself. Therefore, the effective VCE(sat) of the Darlington pair is 1 V or more, resulting in much higher dissipation at a given current level.

Problem 2—Suppose you have some 3-bit data, say, grayscale values for which 000 = black and 111 = white. You have a display device that takes 8-bit data, and you want to extend the bit width of your data to match.

If you just pad the data with zeros, you get the value 11100000 for white, which is not full white for the 8-bit display—that would be 11111111. What can you do?

Answer 2—One clever trick is to repeat the bits you have as many times as necessary to fill the output field width. For example, if the 3-bit input value is ABC, the output value would be ABCABCAB. This produces the following mapping, which interpolates nicely between full black and full white (see Table 1). Note that this mapping preserves the original bits; if you want to go back to the 3-bit representation, just take the MSBs and you have the original data.

3-bit INPUT 8-bit OUTPUT
000 00000000
001 00100100
010 01001001
011 01101101
100 10010010
101 10110110
110 11011011
111 11111111

Problem 3—Can an induction motor (e.g., squirrel-cage type) be used as a generator?

Answer 3—Believe it or not, yes it can.

An induction motor has no electrical connections to the rotor; instead, a magnetic field is induced into the rotor by the stator. The motor runs slightly slower than “synchronous” speed—typically 1725 or 3450 rpm when on 60 Hz power.

If the motor is provided with a capacitive load, is driven at slightly higher than synchronous speed (1875 or 3750 rpm), and has enough residual magnetism in the rotor to get itself going, it will generate power up to approximately its rating as a motor. The reactive current of the load capacitor keeps the rotor energized in much the same way as when it is operating as a motor.

See www.qsl.net/ns8o/Induction_Generator.html for additional details.

Problem 4—In Figure 1, why does this reconstruction of a 20-kHz sinewave sampled at 44.1 kHz show ripple in its amplitude?

Answer 4—The actual sampled data, represented by the square dots in the diagram, contains equal levels of Fsignal (the sine wave) and Fsample-Fsignal (one of the aliases of the sinewave). Any reconstruction filter is going to have difficulty passing the one and eliminating the other, so you inevitably get some of the alias signal, which, when added to the desired signal, produces the “modulation” you see.

In the case of a software display of a waveform on a computer screen (e.g., such as you might see in software used to edit audio recordings), they’re probably using an FIR low-pass filter (sin(x)/x coefficients) windowed to some finite length. A shorter window gives faster drawing times, so they’re making a tradeoff between visual fidelity and interactive performance. The windowing makes the filter somewhat less than brick-wall, so you get the leakage of the alias and the modulation.

In the case of a real audio D/A converter, even with oversampling you can’t get perfect stopband attenuation (and you must always do at least some of the filtering in the analog domain), so once again you see the leakage and modulation.

In this example, Fsignal = 0.9×Fnyquist, so Falias = 1.1×Fnyquist and Falias/Fsignal = 1.22. To eliminate the visible artifacts, the reconstruction filter would need to have a slope of about 60dB over this frequency span, or about 200 dB/octave.