|
Your editor did not realize that the Software Tools for Hams, version 2.0 CD included with his 2008 ARRL Handbook was part of a special, limited-time offer. That CD is not included with copies of the ARRL Handbook sold after that period expired. The CD is still a good deal at $20 from the ARRL Catalog (www.arrl.org/catalog) but is not free. Apologies for the unintentional error.
- "ARRL Handbook"
- "Art of Electronics" by Horowitz and Hill
- "Understanding Basic Electronics" by Wolfgang
- "Experimental Methods in RF Design" by Hayward, Campbell, Bob Larkin
- Trigonometry for Beginners by Stan Gibilisco W1GV
- Learning to Use Rectangular and Polar Notation by Jim Bartlett, K1TX
- Math supplement (PDF) online tutorials and articles on a variety of math topics common in radio
- HAMCALC is a package of software tools to perform many useful calculations.
- The ARRL TIS Web page has a wealth of reference material on building and testing circuits.
- Simulations of electricity and magnetism principles from the Univ of CO - Boulder
- Free online textbooks about topics in electronics
Components
The following PDF files contain the columns as printed in QST. Please check the FAQ section below for any additional information or corrections for the experiments. These files are available to ARRL (Members Only) .
|
Title |
PDF File Size in Bytes |
QST Issue |
Page |
| Experiment #72 -- Return Loss and S-Parameters |
682,729 |
2009 January |
76 |
| Experiment #73 -- Choosing an Op Amp |
227,188 |
February | 73 |
| Experiment #74 -- Resonant Circuits |
467,178 |
March | 72 |
| Experiment #75 -- Series to Parallel Conversion |
344,949 |
April | 75 |
| Experiment #76 -- Diode Junctions |
2,095,352 |
May | 63 |
| Experiment #77 -- Load Lines |
288,001 |
June | 61 |
| Experiment #78 -- Bridge Circuits |
957,811 |
July | 54 |
| Experiment #79 -- Pi and T Networks |
262,679 |
August | 57 |
| Experiment #80 -- Battery Capacity |
341,759 |
September | 55 |
| Experiment #81 -- Synchronous Transformers |
286,417 |
October | 58 |
| Experiment #82 -- Antenna Height |
445,180 |
November | 64 |
| Experiment #83 -- Circuit Simulation, Part One |
176,917 |
December | 48 |
| Experiment #60 -- Smith Chart Fun #2 |
1,034,853 |
2008 January |
62 |
| Experiment #61 -- Smith Chart Fun #3 |
672,532 |
February | 74 |
| Experiment #62 -- About Resistors |
687,128 |
March | 66 |
| Experiment #63 -- About Capacitors |
647,403 |
April | 70 |
| Experiment #64 -- Waveforms and Harmonics |
1,869,764 |
May | 74 |
| Experiment #65 -- Spectrum Modification |
686,020 |
June | 77 |
| Experiment #66 -- Mixer Basics |
672,572 |
July | 71 |
| Experiment #67 -- The Return of the Kit |
607,440 |
August | 69 |
| Experiment #68 -- Phase Locked Loops, the Basics |
725,594 |
September | 71 |
| Experiment #69 -- Phase Locked Loops, Applications |
689,785 |
October | 71 |
| Experiment #70 -- Three-Terminal Regulators |
974,424 |
November | 80 |
| Experiment #71 -- Circuit Layout |
405,488 |
December | 62 |
| Experiment #48 -- Baluns |
762,174 |
2007 January |
56 |
| Experiment #49 -- Reading and Drawing Schematics |
211,158 |
February | 64 |
| Experiment #50 -- Filter Design #1 |
539,666 |
March | 55 |
| Experiment #51 -- Filter Design #2 |
314,219 |
April | 62 |
| Experiment #52 -- SWR Meters |
223,170 |
May | 57 |
| Experiment #53 -- RF Peak Detector |
876,243 |
June | 60 |
| Experiment #54 -- Precision Rectifiers |
254,167 |
July | 53 |
| Experiment #55 -- Current/Voltage Converters |
214,125 |
August | 56 |
| Experiment #56 -- Design Sensitivities |
214,806 |
September | 57 |
| Experiment #57 -- Double Stubs |
1,468,565 |
October | 60 |
| Experiment #58 -- Double Stubs II |
3,120,584 |
November | 67 |
| Experiment #59 -- Smith Chart Fun I |
746,230 |
December | 48 |
|
367,959 |
2006 |
57 | |
|
432,411 |
February |
67 | |
|
276,140 |
March |
52 | |
|
343,683 |
April |
68 | |
|
430,770 |
May |
59 | |
|
333,579 |
June |
62 | |
|
264,456 |
July |
54 | |
|
253,226 |
August |
52 | |
|
233,037 |
September |
52 | |
|
285,659 |
October |
63 | |
|
210,592 |
November |
66 | |
|
591,151 |
December |
53 | |
|
166,379 |
2005 |
64 |
|
|
223,972 |
February |
69 |
|
|
436,870 |
March |
49 |
|
|
127,740 |
April |
63 | |
|
293,789 |
May |
58 |
|
|
159,529 |
June |
59 | |
|
159,384 |
July |
59 | |
|
131,273 |
August |
48 | |
|
625,597 |
September |
62 | |
|
549,277 |
October |
62 | |
|
586,187 |
November |
64 | |
|
725,088 |
December |
64 | |
|
173,096 |
2004
|
61 |
|
|
448,647 |
Feb |
69 |
|
|
141,247 |
Mar |
62 |
|
|
181,382 |
Apr |
71 |
|
|
169,522 |
May |
65 |
|
|
148,284 |
June |
62 |
|
|
253,460 |
July |
63 |
|
|
230,668 |
August |
58 |
|
|
148,106 |
September |
54 |
|
|
250,217 |
October |
62 |
|
|
314,632 |
November |
61 |
|
|
219,431 |
December |
57 |
|
|
195,205 |
2003
|
65 |
|
|
178,736 |
Mar |
64 |
|
|
205,590 |
Apr |
63 |
|
|
169,521 |
May |
59 |
|
|
264,664 |
Jun |
59 |
|
|
277,942 |
Jul |
57 |
|
|
208,456 |
Aug |
59 |
|
|
262,492 |
Sep |
53 |
|
|
209,353 |
Oct |
62 |
|
|
209,503 |
Nov |
72 |
|
| Experiment #11--Comparators |
299,205 |
Dec |
55 |
How Do I Obtain Test Equipment?
What kind of test equipment do I need to perform the Hands-On Radio experiments?
The experiments are written to use the simplest test equipment that can illustrate their fundamental concepts. Many require nothing more than a dc power source and a voltmeter, but more capably-equipped experimenters will get more out of each experiment. Here is a list of the equipment you'll need for most of the work:
At a minimum, start with the voltmeters and the power supply and the function generator. Add an oscilloscope (a great opportunity to share equipment with a friend or club!) as soon as possible. Kits are available for both function generators and power supplies and many are available at hamfests and the online swap sites.
Oscilloscopes
The oscilloscope (or 'scope) the biggest and most expensive piece of equipment - but well worth the investment. This is probably the most versatile electrical instrument of all for general-purpose electronics and RF applications. For a good description of what an oscilloscope is and does, the ARRL Handbook chapter on Test Equipment is excellent reading. More information about using the oscilloscope is available on-line at website.lineone.net/~colin_mccord/Radio/oscilloscope.htm.
The minimum capabilities for a useful oscilloscope is a model with two channels, a probe for each channel (with a ground clip), and the ability to trigger the sweep from either channel. The bandwidth of the 'scope should be no less than 10 MHz, with 20 MHz and up highly recommended. There are literally hundreds of models of these scopes and they are widely available as new devices or used via eBay, eham.net, QRZ.com, numerous other on-line classifieds and at hamfests and swap meets.
How much do they cost? New 'scopes with these capabilities cost from $350 - $500 from several vendors. Used equipment costs a lot less for more performance.On eBay, for example, on most weeks there are several useful scopes that sell for less than $100. Models in this price range are made by B&K, Sencore, Heathkit, Tenma, and Leader. Occasionally, you will see Hewlett-Packard (HP) 100-series or Tektronix (Tek) T900-series scopes, as well. All of these are good units. Avoid older models such as Dumont, Bell and Howell, Eico, Tek 500-series, or any "TV" type scope. If you're willing to spend in the $150 - $300 range, the excellent (and portable) Tektronix 430-series models are widely available.
Probes -- the cables and test clips that are used to connect to the circuit being tested - are also widely available. New ones for general-purpose use cost about $25 and are available from vendors like Jameco or MCM Electronics. If you buy a new 'scope, probes should be included. Used 'scopes may or may not have probes -- be sure to ask. Be prepared to buy new probes as they are the most heavily used part of the instrument and may be worn out.
While there are number of software packages available for PC's that use a sound card as an oscilloscope, they are not recommended for beginners because of the complexities of setting up the software, issues with grounding, and the possibilities of damaging the PC.
USB Oscilloscopes
Traditional oscilloscopes, based on a CRT and all the associated electronics, have gradually morphed into digital oscilloscopes. These scopes convert the input signals to digital data and use microprocessors to perform digital signal processing (DSP) operations so that the waveforms can be displayed on an LCD-type display. USB ‘scopes take the process one step further and move all of the display and DSP software into a regular laptop or desktop PC. The only standalone part of the ‘scope is the analog-to-digital converters packaged in a small pod that connects to the PC using a high-speed USB 2.0 connection.
USB ‘scopes are available in 2 to 4-channel versions, bandwidths into the hundreds of MHz, and up to 16-bit resolution. These are very competitive with low-end digital scopes, requiring only the host PC to provide an amazing variety of functions, including spectrum analysis. This article introduces the Parallax USB ‘scope; an entry-level unit that still provides a lot of functionality.
When using most USB ‘scopes, however, you have to remember that your PC is not isolated from the circuit being tested. Caution is required around voltages high enough to fry the pod and possibly your sound-card input or more! The connection and proximity to your PC may also introduce noise and hum pickup to sensitive circuits. In general, USB ‘scopes aren’t ready for high-resolution, high-precision, low-noise measurements, but these are a rarity in amateur radio applications.
Function Generator
A flexible function generator is a very handy device to have around the bench. The better models have sine, square, triangle, and pulse outputs and cover a frequency range of around 1 Hz to 1 MHz or more. In addition, there may be other features such as frequency sweeping, DC offset, FM or AM modulation, etc. although these aren't used much by hams. Even a generator that only outputs a sine-wave is useful for many experiments or tests.
A new unit from Tenma or Leader will cost around $200, but high-quality used units are widely available for less than $50 on the for-sale Web sites and at flea markets. If you'd like to build your own, entering "function generator kit" into a Web search engine will turn up a wide range of units starting in the low-$20 range.
Do you have an iPod Touch or iPhone? If so, a software function generator can turn these devices into portable function generators! The software application "Signal Suite" can be purchased on the Apple App Store for $9.99. This will download via your computer onto your Ipod touch or Iphone. The application includes noise generators as well as sine waves and other common waveforms. (Thanks, Riley N6BTL
Power Supplies
While you can use your rig's 12-volt supply for some of the Hands-On Radio experiments, a supply capable of supplying both positive and negative voltages (around 12 or 15 volts) would be better. An adjustable supply is the best, particularly if metered. Current requirements for experimenting and building are usually low - 1 amp or less. Suitable used power supplies are available from $15 to $50. A new bench-type adjustable supply with metering and other features will cost from $150 to $250. Unmetered basic adjustable supplies, such as the RSR 3010 (available from Electronix Express) are less expensive - $70 to $100. Kits are also available.
As an alternate to the lab-type supply with meters is an "open-frame" supply intended for use inside equipment. These are typically adjustable only over a narrow range, but often a +/-12 V supply can be found for just a few dollars. Meters can be added or a voltmeter can be used to monitor voltage and current.
Do not try to use a PC supply - they depend on control signals from the PC motherboard and also may be unstable if lightly loaded.
Building Your Own
Start with the ARRL TIS Web page for a selection of projects to build many types of useful equipment. While building your own oscilloscope is "out of scope", so to speak, function generators, power supplies, and all manner of metering and measuring equipment can be easily built by the motivated ham.
In short - all of this equipment is available new or at rock-bottom prices with a little searching. Entering "function generator kit" into a Web search engine will turn up a wide range of units starting in the low-$20 range. Almost every major city has one or more surplus electronics dealers. If you're uncomfortable in buying equipment on your own, it's likely that a club member can help you choose equipment.
You may be surprised at what bargains await you!
As you go through the experiments, the following suggestions assume that you have checked the wiring of the circuit and that all components are correctly connected and of the right values. It always helps to have someone do an "over-the-shoulder" check for wiring errors -- frequently, they'll spot something obvious that you've overlooked. Work with a buddy, if you can.
Please feel free to contribute other answers or tips that you feel would be of value to other experimenters!
I assembled my circuit, but the DC voltages are wrong...
Symptoms
The DC voltages look OK, but my output signal at the load resistor looks wrong...
Symptoms
Common-Emitter Design Spreadsheet
Steve Alpert W1GGN has generously contributed a spreadsheet that performs the calculations required for Experiment #1 - the Common-Emitter Amplifier. This spreadsheet should run under either Linux or Windows.
To use the spreadsheet, enter your operating parameters - Vcc, voltage gain Av, Icq, Vceq, beta, and Vbe. The spreadsheet will automatically compute all of the necessary resistor values to implement a circuit with those parameters. This is an excellent way to experiment with the various parameters and observe the effect on the required components. None of the formulas is locked or hidden so the advanced user will be able to experiment with the design equations, as well.
Steve also has a nifty method of choosing resistors from any of the various tolerance families.
Thanks to Steve for his generous contribution!
Errata
Under "Key Equations", in equation #2 of experiment #1, the last term is "Vcc". It should be "Vce".
In Experiment #2, "The Emitter Follower", the caption for Figure 1 should state that the circuit is a common-collector amplifier, not a common-emitter. Thanks, Dave AD5TU
The text uses the phrase "The reactance of Cf (X =1/2?fc) gets smaller with frequency. That means the impedance of the feedback path between the op-amp's inverting terminal and output also gets smaller with frequency." This is intended to mean that capacitive reactance gets smaller as frequency increases. As reactance decreases, the circuit's gain also decreases, creating a low-pass filter.
A couple of readers have written with questions about their measured frequency response versus what the equations predicted. First and foremost - it is Good Practice to compare predicted versus observed performance and question discrepancies! Don't blindly accept what a model or equation says! If you use software tools to evaluate measurements, you should be sure to understand their output, as well. After all, as Isaac Asimov said, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' (I've found it!), but 'That's funny..."
Gain must be calculated from the actual input and output voltages for each frequency, since the input voltage is likely to change due to changes in circuit input impedance or signal source variation. Performance will also vary from the predicted value if the component's nominal (labeled) values are used instead of the actual values, which can be several percent different.
Avoid very high or very low values of resistance (>100 kohms or <100 ohms) and capacitance (>0.1 uF or less than 100 pF) because the parasitic effects of the way the circuit is constructed or the characteristics of the op amp will affect circuit performance. The simple design equations ignore these effects.
Ron WD8SBB asks, "Could you please refresh my memory about voltage doublers and the potential that they place across the the insulation of the transformer? This is of little issue for low voltages, but for something like a high power tube supply, it would be an engineering issue."
Actually, the voltage stress is the same for both types of multipliers. The peak voltage on the secondary is 1.4 x Vrms in either case because the secondary is never connected across more than one of the capacitors in the charge-pump string. What does increase in the transformer secondary is the current load. The current requirement (versus output current) doubles for a doubler, triples for a tripler, and so forth.
From the ARRL Handbook - "When a doubler is employed, the secondary winding of the power transformer need only be half the voltage that would be required for a bridge rectifier. This reduces voltage stress in the windings and decreases the transformer insulation requirements. It also reduces the chance of corona in the winding, prolonging the life of the transformer. This is not without cost, however, because the transformer-secondary current rating has to be correspondingly doubled."
The instructions for this experiment failed to indicate where the ground clip for the oscilloscope probe was to be connected. For all of the measurements in this experiment, the ground clip should be connected to the SCR's cathode or any lead connected to it.
This brings up an important point about using 'scopes to measure signals in AC circuits. The ground clips are generally connected together, so if they are placed at different points in a circuit, those points are then shorted together through the 'scope ground. The oscilloscope requires a "single-point" ground and will place the circuit at ground potential wherever the ground clip is attached.
This can be a problem - how can you make measurements between two ungrounded points? This is where the 'scope's "ADD" and "INVERT" functions are used. ADD causes the voltages from the two vertical channels to be added together. INVERT causes one channel's voltage to be inverted around ground. The result is that one channel is subtracted from the other. This allows you to measure the voltage between two ungrounded points in the circuit. This is also called a "Differential" voltage measurement.
SAFETY NOTE - when using an oscilloscope to measure voltages on a circuit connected directly to the AC line, you MUST use an isolation transformer on the circuit or on the 'scope. Not doing so can put the full line voltage on circuit ground points, causing short circuits and damage to the circuit or scope, or creating a major shock hazard.
In Experiment #12 on FETs, Jason Dugas KB5URQ noticed that in Figure 2, VO should be labeled with + at the lower end of R1 and referenced to ground. This corresponds to Equation 2. Thanks, Jason!
Wilton Helm WT6C offers some feedback, clarifying the depletion/enhancement mechanics of FETs. "The way I have classified enhancement and depletion devices is: 1) if the thing conducts with no gate bias, it is depletion, if not, it is enhancement. 2) If it is depletion, then the gate will need to be biased negatively to turn it off or to set a class A operating point. If it is enhancement, it will need to be biased positively to turn it on or set a class A operating point. These are assuming N channel devices. For P channel, the polarities would be reversed." Thanks, Wilton!
Wayne Yoshida KH6WZ works for International Rectifier and suggests that readers interested in the IRF510 FET might want to take a look at the IRF Web site, and maybe even sign up for e-mail news. Here is a link to the sign-up page:
Reader Iain Marcuson KC2NLD contributes a drawing more correctly representing the actual structure of the N-Channel enhancement-mode MOSFET. When positive gate-to-source bias is attached to this structure, a conducting region or channel is created under the gate. When the "gate turn-on" voltage is reached, the channel has expanded enough to reach both of the N-type "wells" on either end of the device. Further increases in gate-to-source voltage increase the size of the conducting region, increasing conductivity of the FET.
Ed W3NQN reports that for the first row for 50 & 75 ohms source and load, the circuit designation should be B (not A), since R-source is greater than R-load. Also, in the row for 600 ohm source and 50 ohm load, the Rs value should be 52.2 ohms, not 42. Equation 1 should be 20 log (Vin/Vout) to give positive values for attenuation.
Ed also reminds us that Table 1 can be used to calculate resistor values for impedance levels other than 50 ohms by:
1) Calculating the ratio of the desired impedance relative to 50 ohms, and 2) Multiplying the tabluated resistor values by that ratio.
For example, to use an impedance level of 75 ohms, the ratio would be 1.5 and all resistor values for the 50-ohm attenuator would be multiplied by 1.5.
Bill Taylor N3TR has contributed an attenuator spreadsheet that will automatically calculate the resistor values for symmetrical PI and TEE attentuators. In the light-yellow squares, enter power input, desired input/output impedance, and dB of attenuation required. The orange squares will automatically calculate the required resistances. Substitute the closest standard value resistor for your tolerance requirements. The green squares shotes input and output power, voltage, and current. Note that the orange squares are laid out just as the schematic of the attenuator would be, with the bold black lines connecting them. Thanks, Bill!
Fred Bongard WB6JLL writes, "I am designing an attenuator to match the output of a reference oscillator to the input of my Cushman service monitor.The output of the oscillator has a 1000 ohm impedance and the input of the Cushman is 50 Ohms. The oscillator's output is 1V and the Cushman wants to see no more than .5V input. Unfortunately Figure 3of your article stops at 600 ohm attenuator input and 50 ohm attenuator output."
What I would suggest that you do is "stack" two attenuators together: the first from 1000-to-500 ohms and the second from 500-to-50 ohms. You can scale the attenuators for higher or lower impedances just by multiplying the resistors values by the ratio of the desired to available impedance. For example, to make the 1000-to-500 ohm attenuator, use the values for 100-to-50 ohm attenuators and multiply them by 10. You'll get the same attenuation at the higher impedance. Then make a 500-to-50 ohm attenuator. This will result in the same amount of loss as a 1000-to-50 ohm attenuator. Similarly, if you wanted a 50-to-25 ohm matching attenuator, you would take the 100-to-50 ohm attenuator values and divide them by 2.
Due to lack of availability of 100 uF, 15 V tantalum capacitors, two parts list changes have been made:
Here is a charting spreadsheet that will automatically calculate dB and plot a magnitude and phase frequency response. Enter the frequency, voltage in, voltage out, and phase information into the light-yellow cells. The charts will rescale and plot the points automatically. This is particularly handy to use while you are taking the data so that if a mistake is made or the circuit behaves in an unexpected way, you'll see it immediately. There are instructions for using and modifying the chart in the spreadsheet.
The spreadsheet assumes that you are using frequencies that follow the 1-2-5 rule. If you take additional points, you'll need to use an XE Scatter plot and select "log scale" for the XIII.
Jack W0KPH contributes a more direct calculation of L and T network values. Now that you know how the networks do their jobs, you can use these direct calculations and save time.
Here is a another way to calculate
the L network values:
R1= larger of the
two impedance to be matched
R2 = smaller of
the two impedance to be matched
Xp Parallel
(shunt) reactance in ohms
Xs Series
Reactancein ohms
F in MHz
Xp=R1 /
Sqrt( (R1/R2)-1)
Xs=R2 * Sqrt( (R1/R2)-1)
If the load has reactance, add
the opposite reactance in the series leg with L
To compute
the values for aT network:
X1=Input leg resistance
X2 =Output Leg resistance in ohms
X3=Shunt Leg resistance in ohms
B = 180 - the desired phase shift in degrees (must be between 0 and 180)
Rin=Input R in ohms
Rout=Load Resistancein 0hms
If 90 degree phase shift is wanted then:
X1=X2=X3=Sqrt(Rin*Rout);
If other than 90 degrees is desired then the formulas become:
X1 = (-R1/tan(B))
- X3
X2 = (-R2/tan(B)) - X3
X3 = Sqrt(Rin*Rout)/sin(B))
Again if the load has some reactance add the opposite reactance in the output leg....
To convert
either X to pF of capacitance, C = 10^12 / (2*Pi*F * X)
To convert either L to uH of inductance, L = 10^6 * X/ 2*Pi*F
These equations came from the paper, "Matching Networks and Phasing" by W.C. Alexander, Crawford Broadcasting Company.
The following is relayed by Paul Wolcott WD8H.
This experiment reminds me of an output stage used in broadcast products. The circuit was a variation of the one shown in Figure 1B, and was used as a current booster on the output of an op-amp. That way the op-amp circuit could drive a step-up output transformer up to levels of about +24 dBm when powered by +/- 20 volts. In this application current consumption (with the attendant problem of thermal dissipation) and crossover distortion were both considered critical parameters.
1) The push-pull circuit along with the op-amp was placed inside the op-amp's gain controlling feedback loop. (Meaning that the feedback resistor - see Experiment #3 - was connected to the load and the push-pull circuit was between the op-amp output and the load.)
2) The op-amp we selected was an LM318, which at the time was the best mix of a fast op-amp with fairly high current output, later replaced by NE5534 op-amps.
3) We connected a low value resistor, usually 68 ohms, from the op-amp output (junction of D1/D2 in Figure 1B) to the Vout point.
4) The values of R1/R2 were carefully selected to have Q1/Q2 just barely turned on. (D1/D2 could also be replaced with low value resistors, about 150 ohms, in some applications.)
The result of all this was that when the input signal was in the crossover region of Q1/Q2, the op-amp was able to supply some current directly into the output through the 68 ohm resistor. This did not eliminate but did tend to greatly reduce the crossover distortion while keeping the heat dissipation of Q1/Q2 under control. Another factor which also reduced distortion was the feedback loop in the op-amp circuitry which compensates for non-linearities in the output stages. We used to measure distortion (% of THD + noise) on an audio console using several of these stages plus several transformers etc. as consistently below .07% at 1 kHz and below .15% for the entire range of 30 Hz to 20 kHz.
Charles, VE3CQH, noticed an error in Figure 3. The lower MOSFET should be labeled P-Channel instead of N-channel.
Ralph K1RD spotted an error in the Lissajous Figure section of the experiment. The value given for the capacitor in Figure 1 (0.01 uF) is too small - it should be 0.1 uF. The printed value of the capacitor gives only one-tenth the intended phase shift. (You can also get the proper value of phase shift at 10 kHz.) The actual value of small ceramic capacitors is usually somewhat larger than their nominal value, so you get from 30 to 50 degrees of phase shift.
New link for Colin Mccord's oscilloscope tutorial
Solutions for Experiment #29 circuit analysis:
1) Calculate Req by first adding the 330 and 100 ohm resistances to get 430 ohms. Combine the parallel resistances of 430, 470, and 1 kohm to get 183 ohms. This resistance replaces everything connected to the voltage source.
2) The current supplied by the voltage source is 12 V / 183 ohms = 65.5 mA
3) The current through each of the branches is as follows:
Through the 470 ohm resistor, I = 12 / 470 = 25.5 mA
Through the 1 kohm resistor, I = 12 / 1000 = 12 mA
Through the 430 ohm combined resistors, I = 12 / 430 = 27.9 mA
As a check back to step two, add the three currents together to get 65.4 mA (the difference is due to rounding).
4) Use the voltage divider equation to get the voltage from node 1 to 3:
V = 12 (1 - 100/430) = 12 (0.768) = 9.22 V
The voltage from node 3 to 2 is the remaining voltage from the previous step, V = 12 - 9.22 V = 2.78 V
Equation 2 was misprinted in the QST version of the column - an extra set of parentheses was added. It should be:
VL = VS - I RS = VS - VS RS/(RS + RL) = VS [ 1 - RS/(RS + RL) ]
Thanks to reader Ken Stewart KC0TOB
Stu K2QDE noted that the bridge rectifier wiring shown on the Astron schematic was incorrect. The correct wiring uses only half of a regular bridge with the ac transformer output connected to the ac bridge inputs and only the + output connected to the pass transistors and filter capacitor.
Only half of the bridge's diodes are used, so it's used as a full-wave, center-tap rectifier, not a bridge. The reason the part is used this way is that it is less expensive than a pair of standalone diodes, I suppose. Stu also noted that the proper URL for the rectifier data sheet is http://www.diotec-usa.com/35dbp.PDF.
The schematic for the pulse generator in Figure 3 of the QST article is incorrect. There should have been a 1 kohm pull-up resistor to +12 V and a small, current-limiting 100 ohm resistor connected to the switch. This version of the figure is correct. Thanks to reader L. Raymond Pearl, AA7IH for catching the error!
When confronted with an unlabeled seven-segment LED module, Wayne AB7O discovered that he could figure out the wiring "by eye". Assuming that he had a common-cathode display, he grounded a pin and applied a few volts of positive voltage (thru a 470 ohm resistor) to each other pin in turn. If no segments light up, ground the next pin. Once the common cathode pin is identified, apply voltage to each of the other pins and label according to which segment lights. If grounding each pin in turn lit no segments, the chip would be a common anode and can be tested by changing the polarity of the applied voltage.
In Experiment #38, the final bullet point. under "Testing the Charger", the value of R3 should be RAISED to lower charging current. Thanks to Larry Joy WN8P for that correction. Also, to slow down the charging of a capacitor used as a battery simulator, increase the value of the capacitor. Any size can be used as long as the working voltage is greater than that of the power supply.
In Experiment #39, Figure 3 should show the combination of R1 and R2 as a potentiometer with the wiper connected to pin 2 of the LM311. The portion of the potentiometer element to ground takes the place of R2 in Figure 2 and the other portion takes the place of R1. Also, in the section 'Getting and Indication', references to R6 should be to R7. Figure 3 shows Q3 as a 2N700. That is incorrect - the transistor should be a 2N7000.
There is an error in the pin diagram for the 2N4416 in Figure 1. Counterclockwise from the tab in the bottom view, the connections are Source, Drain, Gate, Case. The author regrets any frustration and ruined components this may have caused. The correct diagram can be confirmed in the ARRL Handbook's chapter on Component Data and References.
Q: Tom N4WBS asked, "Can I use a larger (or smaller) toroid for the output transformer?"
A: You'll need fewer turns to get the same reactance in the primary, but it's the ratio that's critical in this design. The ARRL Handbook has a table of toroid data with a formula for inductance for a given number of turns. Find the reactance of the existing 12-turn primary and then find the number of turns on your toroid that give about the same result.
Q: Aryeh KA1PB/4X1PB caught the HOR mis-statement that the bias resistors are chosen so that the impedance of the two resistors in parallel is 10 times that of the emitter resistance.
A: The bias resistors should be chosen so that the current through the bias resistors is 10 times the dc base current. Depending on the dc beta of the 2N3904, base current for a 5 mA collector current will be 20 to 50 µA. Current through the bias resistors is about 450 µA. HOR regrets the error!
The first term of the equation for gain of the Class C amplifier is (Vcc - Ve)2, not (Vcc*Ve)2. Thanks to Tom N4WBS for picking up this typo.
Jack N4UY built the closely-related Tuna Tin II transmitter and added his own chirp-reducing keying circuit. More information can be found at http://mysite.verizon.net/vze1oa8r/TTMods.html.
The FT50-6 toroid referenced in the article should have been a T50-6 powdered iron core - your editor regrets the error.
Mike Daenhe DF1ZN is using the free version of SPICE from Linear Technology to simulate some of the circuits in Hands-On Radio. A description is on his home page at http://www.df1zn.de/simulation/simulation.html. You can download the SPICE schematic file at [hyperlink to CLEGG.ASC] or look at the screen shots in the following files:
Earl N8ERO contributes the URL of a Web page (www.radio-electronics.com/info/circuits) with a table of suggested values for crystals between 1 and 20 MHz in a transistor Colpitts oscillator. Click on "transistor crystal oscillator" to read the entry.
Bob VE3OSZ noticed that the formula for L inductance incorrectly showed "n2" instead of "n-squared", although the derived formula for n is correct. For reference, the correct formula can be reviewed in the ARRL Handbook tables of inductance/turn factor.
Tom Rauch W8JI caught a mistaken reference in the section title "Building a 4:1 Current Balun." (That section was originally intended to describe a current balun, but the inattentive author changed his mind and not the title.) The 4:1 balun described in the column does transform impedance, but it is a VOLTAGE balun because the transformation is performed by combining inverted voltages at the end of the transmission line. The statement in the caption for Figure 3 that currents are "equal and opposite" assumes perfect load balance, as well. From W8JI, "Voltages across the windings are equal and opposite, but currents [in the windings] can be in any proportion depending on load unbalance. That system really forces equal and opposite voltages. It actually functions as a phase inverting ransformer with A A' being the primary that is ALWAYS at input voltage and B B' always at the same voltage but 180 degrees out of phase by the reversed leads. The current ratio can be anything the load wants as long as the load has equal voltages (assuming no flux leakage)." Tom's Web site has a lot of good information about baluns and many other things - highly recommended.
Vackar VFO, Figure 10.15 from the 2007 ARRL Handbook
Tick-4 Keyer, Figure 19.34 from the 2007 ARRL Handbook
Filter design authority Ed Wetherhold W3NQN wrote to point out an error in the design equations that exists in the ARRL Handbook, as well. On page 56, equations 1 and 2, the normalized units are implied to have units of ohms and radians/second. This is not so as normalized values have no units - so fc is simply 1.0, not 1.0 rad/sec or 1.0 Hz or anything else... just 1.0. The ohm symbol was used to clue the reader as to the origin of where the "1" came from, but the implication that it carries units of ohms is incorrect. The description of the scaling process was abbreviated due to space considerations and Ed recommends that the interested reader study the filter design process in Chapter 12 of the ARRL Handbook for a more complete and nuanced discussion than is possible in a two-page column. The author heartily concurs and wishes to thank Ed for his remarks.
Design solutions for a series-input 7 MHz fc, 200 ohm low-pass Butterworth filter:
Design solutions for a 3.8 kHz fc, 32 ohm low-pass Butterworth filter:
For more experimentation with LC filter design, try the Web site of Tony Fisher where you can find an interactive design page.
Ed Wetherhold W3NQN caught your editor crossing his terms: "Return coefficient" is incorrect. What was meant is, of course, "reflection coefficient". Return loss is another way of measuring transmission line mismatches.
Ed also correctly points out that the conversion from low-pass to high-pass requires that reciprocals of the normalized values be used. That means the when the components are interchanged, L for C and vice versa, the normalized values are replaced by their reciprocals. For example, the transformed value of C1 that replaces the original L1 is not 0.7654, but rather 1/0.7654 = 1.3065. Follow the math through and you'll wind up with the 6 uH inductor replacing the original capacitor for the shunt-input design. Thank you, Ed!
In the band-pass section of the column, in Figure 3 there should have been a resonating capacitor across the 44.2 uH inductor with a value of 11.2 pF. In this design, every series or shunt connection should be a parallel or series LC-circuit.
And W3NQN also clarifies that the "alternate type of Chebyshev" (note the -shev spelling, widely used) is also known as an "elliptic" filter because of the equations used in its design. This filter type has attenuation troughs and peaks in the stopband, where the Chebyshev has ripple in the passband.
Clarifying how Rd of the detector diode is calculated (referring to the fifth paragraph of the section "The Envelope Detector") - The forward resistance for the diode, Rd = change in Vf / change in If. (See the third sentence of the paragraph.) To find the amount of change for voltage and current , pick two points from the data sheet at which Vf and If are known: Vf=0.52 V & If=0.1 mA and Vf=0.62 V & If=1.0 mA.
Change in Vf = 0.62 - 0.52 = 0.1 V
Change in If = 1.0 - 0.1 = 0.9 mA
Rd = 0.1 V / 0.9 mA = 111 ohms
Earl N8ERO wrote to ask why some authors show the precision rectifier with a small (30 pF or so) capacitor across the diode to prevent oscillation. The oscillation occurs sometimes when the diode is cut off (in a high-impedance
state) and the circuit is in a high-gain mode. It depends a lot on the layout and the particular op-amp. Similarly in the full-wave circuit, if the diodes have identical characteristics, it's possible for the circuit to have a short period during which both diodes are in a medium impedance state, upsetting the gain of the circuit until one diode starts to turn on more. It's obscure, but if one plans on manufacturing a product with the circuit, it could be important.
Art KN3U sent the following notes about color codes and part marking:
"Parts with 5, 10, or 20% tolerance are usually marked with three digits. Precision parts (1% or better tolerance) are generally marked with four digits, giving them an extra significant digit. For example, a resistor from your junk box marked "4994" is "499" followed by four zeroes, or 499 0000. Rearrange the spaces and you have 4 990 000, or 4.99 megohms. There is a catch for values less than ten ohms, picofarads, etc. The system described above has no provision to encode such low values. For example, "680" is 68 with no zeroes after it, or 68 ohms, picofarads, or microhenries. What does one do if one has a 6.8 ohm resistor? One solution is simply to print the value, "6.8 ?". But it is easy to overlook the decimal point. So it has been customary to use the letter "R" as a proxy for the decimal point when the value is less than 10 ohms (less than 100 ohms in the case of a 1% resistor). The code for a 6.8 ohm 5% resistor under this scheme would be "6R8", and the code for a 6.81 ohm 1% resistor would be 6R81. If the resistor is marked using color bands, the decimal point is usually represented by a gold band."
Louis VE2EZD noticed an error in my capacitor value explanation. The marking "103" actually means 10 x 10^3 pF, not 1 x 10^3 pF. The value is 10,000 pF = 10 nF = 0.01 µF.
Lynn NX6B reminded me of another type of value - the "available value"!
(Also known as the "junk box value".) This is the value of a component that you can actually obtain, as opposed to what you wanted. You may want a 4.3 kohm resistor, but you can't seem to find one at your favorite parts store and the junk box only has 4.7 kohm resistors - so that's what you use.
Lynn's note reminded me of several similar values:
The equation printed for the open stub's impedance is incorrect.
The correct equation is XC = ZO cot (LE + 90) or XC = -ZO / tan (LE). A complete discussion of both equations is included in experiment #58.
George W2VJN notes that "double stubs" is usually taken to mean a pair of identical stubs used as filters to give more attenuation than a single stub. He also cautions the user to be sure that the proper velocity factor is used for the actual coaxial cable used - check with the manufacturer if you are unsure.
The best way to connect the double stubs is to avoid a direct common connection as shown in Figure 3 of the experiment. He recommends that each stub be cut individually first, then a separate T-adaptor be used to connect each stub to the transmission line. (This is fully described in George's book "Managing Interstation Interference" http://www.qth.com/inrad/book.htm. Look for Figure 28 and the associated text.) Doing so prevents unwanted interactions in the stubs.
The original tutorial reference for Lissajous figures has "gone dark". A similar on-line reference can be found at http://www.visionics.ee/curriculum/Experiments/Electronic%20Measurement/LissajousPattern1.html.
In addition, in the text on making the measurements, the instruction to "center the ellipse on the horizontal axis" means "center the ellipse vertically". This could be mis-read. Here are the same instructions, reworded for clarity: "You'll see an ellipse instead of a straight line because the output signal is not an exact replica of the input. It's delayed a few microseconds by the R-C circuit and somewhat lower in amplitude. With the ellipse centered on the oscilloscope's graticle scales, measure both the outside height and where the ellipse crosses the center scale. Convert these measurements to a phase difference with [the arcsin equation]" You may be more familiar with the arctan formula that uses the ellipse's scale crossings on both axes. This method is a little easier to use, but both methods are equivalent.
Table 1 was generated with minus and plus signs reversed. A correct version of the table can be downloaded here.
Experiment #58 reminded John K4ERO of some work he did a few years ago for notching out ANY frequency, whether it is any harmonic or not. With the way to arrive at the appropriate lengths being simple, even those not familiar with the Smith Chart can cut the lines to the correct length. It works like this:
If the notch frequency is above the pass frequency, begin with a quarter-wavelength of coax at the pass frequency. Cut enough off this quarter-wavelength to make a quarter-wavelength at the notch frequency. This piece is left open, and the leftover piece is shorted. The two pieces in every case will be such as to cancel each other at the pass frequency, just at the two examples in the QST article demonstrated. If the notch frequency is less than 105% of the pass, losses may be high, since the shorted section will be very short at the pass frequency. There is no upper limit on the notch frequency.
If the notch frequency is to be lower than the pass frequency, begin with a half-wavelength of coax at the pass frequency. The coax is then cut to a quarter-wavelength at the notch frequency, and the two stubs installed, with both of them being open. This works for a notch frequency down to 1/2 of the pass frequency, and up to about 95 percent of the pass frequency before the losses get out of hand.
The stubs are then both installed directly on the feed-line.
For even lower notch frequencies, this method can be extended by using either 3/4 or 1 wavelength at the pass frequency and leaving the two pieces either open or shorted as appropriate. All these methods make some other "extra" notches, which are typically not a problem and may be useful. The smallest difference between the pass and notch frequencies depends on the quality of the coax and the allowable loss. The 5% value is chosen somewhat arbitrarily. For receive only, loss is hardly a problem.
He has used this method to notch out broadcast QRM from very powerful nearby stations that were causing front end overload. It was used to notch 15.115 MHz transmissions out of a 20 meter band receiver with hard line coax. This method is used in commercial short-wave diplexers made entirely of transmission line, for example to put two transmitters on one broadband antenna, or to put the output of one transmitter on either of two antennas without switching. (Each antenna on a different shortwave band). In these high power applications the lines are often open lines, and the frequency separation 20% or more.
The construction of the circle on the Smith Chart also illustrates why adding transmission line will not change SWR. As line is added or subtracted, the impedance point will move around the chart at a constant radius from the central point, but never get any closer (or farther away).
Feedline loss does eventually make the point spiral in towards the center, but quite slowly. The reason changing feedline length may allow a tuning unit to achieve a match is that the impedance point has been moved into a region of the chart in which the impedances are easier to match. This depends on the circuit of the tuning unit and the values of its component.
Another reason may be that there is RF current flowing on the outside of the coax, upsetting the sensing circuits in the tuning unit. In this case, changing the feedline length also changes the amplitude of the current on the outside of the line, changing conditions inside the tuning unit, as well.
Jim Summers, KD7F, notes that the labeling on many of the Smith Charts that can be downloaded from the Web have an error. The top half of all Smith Charts (everything in the "northern hemisphere" above the resistance axis) is inductive - whether reactance or susceptance. This error tripped up the HOR author, as well, who ignored the little voice in his head yelling "Capacitance in parallel moves south, not north!"
Jim writes, "In (the original article's) Figure 2, it takes shunt inductance (not capacitance) to move from point A to point E. All points above the line of zero reactance on the chart are inductive, and all points below are capacitive. These charts would seem to say that the top half of the chart represents inductive reactance or capacitive susceptance - which makes no sense. A series R and L will have an impedance which when converted to an admittance can be represented as a parallel R and L - not a parallel R and C!
"The confusion probably arose from the method used to convert impedance to admittance using a Smith chart with impedance coordinates only - reflecting the reflection coefficient vector through the origin. When you do this, an inductive reactance in the top half of the chart becomes an inductive susceptance in the bottom half of the chart - but in this case the circles don't move - they still look like the impedance chart but now represent admittance.
"This isn't what is going on when both admittance and impedance circles are on the same chart. The admittance circles are already reflected through the origin (effectively rotating the chart 180 degrees) so inductive reactance and inductive susceptance are in the same region of the chart. The points above the zero reactance/susceptance line have positive reactance and negative susceptance (which is inductive in both cases). The points below the line have negative reactance and positive susceptance (which is capacitive in both cases). A "real" Smith chart (from the Analog Instruments Company, PO Box 950, New Providence, NJ 07974 ) with both sets of circles states this clearly." Thanks for clearing that up, Jim!
Steve K6UM spotted a plus-minus reversal in the first paragraph on page 75, describing the value of the impedances at points B and C. (For those of you following along in the Hands-On Radio Anthology book, that would be on page 114.) The value of impedance at point B is 1.0 - j1.4 ohms (the original text says +j1.4 ohms) and at C the impedance is 1.0 + j1.4 ohms (the original text says -j1.4 ohms). Your editor regrets the error.
The reference value of permittivity used to calculate capacitance is most frequently stated as the "permittivity of free space" although the terms "permittivity of empty space" and "dielectric constant of vacuum" are also used. (http://en.wikipedia.org/wiki/Permittivity_of_free_space) The international standard (still catching on) is to use the term "electric constant". The value for all is the same - 8.854 x 10-12 farads/meter. Free space itself is an interesting theoretical construct (http://en.wikipedia.org/wiki/Free_space), but as far as capacitance goes, the dielectic constant of vacuum is 1.0 and that of dry air at standard temperature and pressure is 1.00054 - effectively the same value for amateur purposes.
Electrolytics - the dielectric is actually a film of oxide formed during manufacture on the electrode designated as the anode (similar to the tantalum capacitor). The electrolyte gel makes contact with the dieletric film so that the cathode electrode is connected directly to one side of the extremely thin dielectric film. (Thanks, Bill W6TM)
A couple of errors crept in - the breakdown voltage of air is 30,000 V/cm, not 30,000 V/in as stated on page 71. Also on page 71, the correct relationship between lead orientation and construction is that axial leads (leads that come out of the ends of the capacitor along its axis) indicate roll-type construction and radial leads (leads that come out of the capacitor at right angles to its axis) indicate stack-type construction.
Figure 3 also does not show the second layer of dielectric under the bottom electrode layer. This second layer is necessary to keep the electrodes from shorting out when rolled up. The layer was omitted from the illustration because it was thought to be confusing since this was not a construction article for building a capacitor. Nevertheless, there are two distinct dielectric layers required in an actual capacitor. (Thanks to Dick K2RIW for his observations)
Your editor did not realize that the Software Tools for Hams, version 2.0 CD included with his 2008 ARRL Handbook was part of a special, limited-time offer. That CD is not included with copies of the ARRL Handbook sold after that period expired. The CD is still a good deal at $20 from the ARRL Catalog (www.arrl.org/catalog) but is not free. Apologies for the unintentional error.
Here is the (spreadsheet) "Fourier Demonstration" for experimenting with components of waveforms.
Configuration Information:
"Signal Generator"
Channel 1 and 2 - set to FUNC and select waveform, select frequency range as required by the experiment, adjust Function Display to desired frequency.
Control - set both channels ON, set output to maximum clockwise, set Volume 1 slider to full Left (L), set Volume 2 slider to full Right (R)
"SpectrumView"
Default settings should be used, plus:
Click "Start" to begin displaying frequency
Leave Vertical Display on Log_10 and Vertical Scale on 10 dB/division
Use sliders under display to set minimum (left-most) and maximum (right-most) frequency
"USB Oscilloscope Version 4"
Follow installation instruction in Help to select the proper COM port ID for the scope to be recognized by the software.
Perform the ground calibration as prompted by the installation procedure.
Horizontal should be 200 usec/division
Vertical sensitivity should be 100 mV/division
Trigger tab under display - set Trigger Edge to "rising" and Run/Stop Mode to "continuous acquisition"
Click "Run" next to horizontal control to begin measurement in the time domain
Click "FFT" to begin spectrum measurements, click "Run/Stop" in Optascope FFT window to display spectrum
Click "Scope" to close spectrum window and return to time domain display
URLs for the data sheets in the original articles have changed. The LM565 datasheet can be downloaded from http://www.national.com/JS/searchDocument.do?textfield=LM565&categories=Datasheets.
The application note AN535, "PLL Design Fundamentals" is available from http://www.datasheetcatalog.com/datasheets_pdf/A/N/5/3/AN535.shtml. (Thanks, Dino KL0S)
In the parts list, the capacitor value shown as 0.022pF should be 22 nF (0.022 uF).
A reader commented, "I ... basically understand how the PLL tracks the input signal. The only thing that seems strange is that the VCO output at pin 5 (of the NE565) is a square wave, not a sine wave, at the proper frequency."
All is well because the VCO output is, in fact, a square wave. (To use the VCO output signal as an oscillator, the harmonics of the fundamental would have to be filtered out.)
It may help to think of the phase detector as a switch, controlled by the VCO output signal. When the switch is on, the input signal passes through to the loop filter. The dc component of that switched input signal is what creates the error signal to the VCO.
If the input and VCO signals are in phase, the output of the phase detector will be a maximum because the switch will be on for the half-cycle of the input sine wave that is positive (just like half-wave rectification).
If the input and VCO signals are out of phase, the opposite half-cycle of the input will make it through to the loop filter and the output is a minimum.
If the input and VCO signals are 90 degrees out of phase, then the resulting dc component is zero because half of each input half-cycle makes it through - half above and half below zero.
Different types of PLLs may invert one of the signals or shift its dc values to suit the exact circuitry, but the idea of varying the error signal by varying the period during which the input signal value is evaluated is common to all PLL's.
Howard KF6NOR notes that, while it may be possible for a particular manufacturer's version of the LM317 to supply 3.4 A (National Semiconductor), the typical limit is 2.2A and may be as low as 1.5A. Quite true - check the data sheet from the manufacturer before making any assumptions about maximum current. The biggest challenge for the regulators is generally adequate heat dissipation, limiting the amount of current through the IC.
The following photos show the completed regulator and the assembled go-kit.
A close-up of the regulator, built on a scrap of PC board.
The LM-317 regulator IC is mounted directly on the enclosure - a home wiring junction box. (An insulating mounting kit is required.)
The go-kit with the external power connection.
The regulator assembly is attached to the wall of the container and the two power indicators can be seen through its translucent wall. A barrier strip is used to distribute power to and from the regulator.
Inside the go-kit, the radios and battery charger are all attached to the terminal strip through Powerpole connectors and jumpers.
Accessories are kept on a shelf over the radios that fits on top of the internal "shoulder" of the container.
Al Wolfe K9SI writes in with a tip about keeping 6 V and 12 V connections from being accidentally connected. "As the National Electrical Code recognized years ago, that it should be impossible to plug something into the wrong voltage or current receptacle. Therefore, they set up the many standards for different kind of plugs and receptacles for power distribution. A simple solution to the PowerPole dilemma would be to stack the Powerpole terminals vertically for the lower voltage instead of the more common horizontal method. That is, with the terminals parallel instead of in the same plane. This should reduce the possibility of plugging in the 6 volt devices into the 12 volt supply by mistake."
The topic provoked a discussion of conventions for whether Return Loss is a positive or negative number. Like attenuation, the numeric value is sometimes given as positive ("20 dB of attenuation") or negative if only the calculation is performed. ("10 log (Pout / Pin) = -20 dB") To be completely correct, it should be acknowledged that the official definition of Return Loss is:
RL = -10 log (Reflected Power / Forward Power) = -20 log (Reflected Voltage / Forward Voltage)
The negative sign means that if the load absorbs some of the power, then RL will be a positive number. However, this convention is not strictly followed and you will encounter RL given as negative numbers in data sheets and even on instrumentation. Don't be confused, just as you are not confused if someone says, "Attenuation was minus twenty dee-bee..." They are not intending to say that there was 20 dB of gain! Your HOR editor pledges to give RL as a positive number in the future.
S-parameters, as you might expect, are considerably more complicated than the introduction provided in this experiment. For example, the proper name for S11 is the Input Voltage Reflection Coefficient. S21 is the Forward Voltage Transmission Coefficient. Because there can be a phase shift when power is reflected from or transmitted through an interface, these coefficients are actually complex numbers. They can be represented in either x+iy form or as phasors (polar notation) with a magnitude and phase angle. In the latter case, Return Loss is equal to the magnitude of S11 and a device or circuit's gain is equal to the magnitude of S21. A thorough discussion of s-parameters is available for downloading as a PDF document from the Agilent Corporation - "AN154 - S-Parameter Design"
And a math gremlin snuck into the calculations for Table 3 when the "squared" exponent in the fourth formula was not accounted for, leading to the values of RL being one-half of what they should be. (The log of a squared value is the same as twice the log of the unsquared value. ie - log x^2 = 2 log x). The correct values for Table 3 are as follows:
SWR Prefl/Pfwd RL(dB) 1.01 0.00002 -46.1 1.1 0.00227 -26.4 1.2 0.00826 -20.8 1.5 0.04000 -14.0 2 0.11111 -9.5 3 0.25000 -6.0 5 0.44444 -3.5 10 0.66942 -1.7 100 0.96079 -0.2
HOR wishes to thank Ed Wetherhold W3NQN and Igor Kosvin, KB1QOV for their feedback.
The voltage gain of the amplifier in Figure 1 was miscalculated in the article as 10 (20 dB), but it's actually 1+ Rf/R = 11 = 20.8 dB.
Gene KB6KRI sent in a graphical technique of series-parallel and polar-cartesian conversion shown in this figure. Gene notes that this method was used in conjunction with impedance measuring equipment that gave results in the polar format of magnitude (Z) and angle (theta). It works in both 'directions' between and series and parallel equivalents.
To convert from polar to cartesian coordinates, read the projection of the Z,theta line on the axes.
To convert from cartesian to polar coordinates, plot the point R,X and draw a line to the origin. It's length is Z and the angle between it and the x axis is theta.
Series to parallel conversion:
1) Plot the polar form of the impedance: Z and theta.
2) Read the values of Rs and Xs as the projection of the Z,theta line onthe x and y axes, respectively.
3) Draw line AB so that it makes a right angle with the line drawn fromthe origin to Z,theta.
4) Rp and Xp are the points A and B.
Parallel to series conversion:
1) Plot Rp and Xp on the x and y axes, respectively.
2) Draw line AB.
3) Draw a line from the origin to AB such that it makes a right angle to line AB.
4) The intersection of the two lines is the point Z,theta.
5) Rs and Xs are the projections of the Z,theta line on the x and y axes, respectively.
Download the set of typical output characteristic curves for a 2N3904 transistor. The load line is drawn between Vcc on the Vce axis and Vcc/(Rc+Rc) on the Ic axis.
There is an error in Figure 2 and the associated text to its right. The equation for Zx should be Zx = (Z2/Z1) x Z3. Z2 and Z1 were swapped during a drawing revision and the equations were left unchanged.
Stan WA2PUO writes with a neat application of bridge circuits to make a "dynamic bridge squelch". "Back in the bad old days, back when I was a junior tech part time after school at the local TV/car radio repair shop, we had an old (not then, though) Heathkit CB lunch-box. It used a preamped super-regen receiver, complete without squelch. Hissssss all the day long. Then an article in a radio-oriented magazine offered a respite -- a dynamic bridge squelch. It consisted of two 47-ohm 1/2-watt resistors and two #47 panel lamps (6.3 V @ 150ma.) configured; Z1 (from the article) 47 ohms, Z2 and Z3 a lamp, ZX the other resistor, the speaker was the galvanometer, the output transformer the source. You turned up the volume until the lamp's warm resistance equaled the fixed value and the Hisssssss went away. Then, when a real voice was received, the lamps warmed all the more and we heard the voice loud and clear. The lamps even blinked in time with the syllables! Neat? It had a nice soft squelch "knee" to boot."
This handy spreadsheet allows you to enter values for the resistances to be matched and the frequency range over which the network must operate.
George VE3ERP sent a note reminding us that his HAMCALC software package (version 112) has added the necessary tools to manipulate Pi and T networks as of 3 August 2009 under Menu E. You'll find lots of useful goodies in this software - available for downloading at www.cq-amateur-radio.com.
In the Table of Battery Types, "Nominal Voltage" is just a value used for referring to the battery chemistry and construction and is not a guaranteed performance specification. It's similar to the terminal voltage, Voc, referred to in the text.
The upper voltage curves in Fig 1 are at higher voltages due to the smaller voltage drops across the internal battery resistance with smaller currents. In Figures 1 and 2, the curves start at a higher voltage and rapidly drop to a steady value because when the battery is brand-new, fresh chemicals are close to the surfaces of the electrodes, providing high currents at a high terminal voltage. This only lasts for a short time as the surface chemicals are depleted, requiring the electrons to flow through a longer distance, also raising internal resistance, and causing the terminal voltage to fall.
Regarding the energy-consumed amounts in Fig 1, the caveat is that 3.25 V is chosen as the end-of-life voltage. Under heavy load (4900 mA), the battery voltage drops to 3.25 V when 2100 mAhr have been consumed. Thus, available capacity for that battery under that load is 2100 mAhr. If the same battery is discharged at a lighter load (490 mA), more energy can be consumed before the end-of-life voltage is reached.
(Thanks to Fred WL7IJ for his observations)
To verify the solution shown in Figure 1, Tom N0GSG used a Smith chart emulator for the TI-85/86 calculators that he has written. Tom generously offered to share this application with other hams using these calculators.
A reader wrote to asking about the dipole gain values in Table 1. How do I arrive at these gain figures? ~7dBi for a dipole seemed awfully high for a dipole. That's a good question! The "extra" gain comes from ground reflections that reinforce the usual "doughnut" pattern. In free space, a dipole has 2.1 dBi gain, but over a reflecting ground, up to 6 dB of additional gain is possible for a maximum total of 8.1 dBi. "Ground gain" can also inflate claimed antenna gains because, ss the column shows, actual gain depends height and ground quality. Use free-space gain figures when comparing antenna gains to eliminate ground reflections as a source of error in the comparison.
Barry W6YE sent the following animated GIF files that show the radiation patterns for dipoles of varying lengths. By clicking on the hyperlink, your browser will display the animation.
Linear Dipole Gain - shows dipole gain on a linear scale
Normalized Dipole Gain - always places maximum gain on the outer ring
The graphs show the number of lobes increasing with length - these are referred to as "grating lobes" and they are created as more and more current maximum appear along the antenna, one-half wavelength apart. The original Mathematica program used by Barry was created by Takuichi Hirano of the Tokyo Institute of Technology.
