|
|
|
|
|
References and further reading for Chapter 5.
|
[1] Transmission
Line Transformers Handbook. Jerry Sevick, W2FMI, Amidon
Associates Inc. 1997. [2] Building and Using Baluns and Ununs. Practical Designs for the Experimenter" (2nd printing 1995) Jerry Sevick, W2FMI, CQ Communications 1994, ISBN 0-943016-09-6. [3] Transmission Line Transformers (4th edition 2001) Jerry Sevick, W2FMI, Noble publ., ISBN 1-884932-18-5. Jerry Sevick W2FMI, balun articles in Communications Quarterly: [4a] "Baluns Revisited", Summer (July) 1992, p13-18. [4b] "The 4:1 Balun", Fall (Oct) 1992, p23-29. [4c] "6:1 and 9:1 Baluns", Winter (Jan) 1993, p43- 51. [4d] "1.5:1 and 2:1 Baluns", Spring (April) 1993, p39-44. [4e] "The 12:1 Balun", Summer (July) 1993 p36-38. [9] "Automatic Tuning of Antennae". M J Underhill [G3LHZ] and P A Lewis. SERT Journal, Vol 8, Sept 1974, p183-184. Reprint of paper in Mullard Research Labs Annual Review, 1973. Introduces the idea of using phase, resistance, and conductance for unambiguous adjustment of the matching network in automatic antenna tuning systems. Describes the matching process using Z-plane diagrams, and operations involving lines of constant resistance and circles of constant conductance. Advocates the use of a π-network with one or other of the capacitors set as near as possible to zero capacitance (i.e., using the π-network as an L-network, but without the need for switching), on the basis of minimised voltages and low-pass filtering. Notes that the input impedance of a 'typical' antenna operating between 1.5 and 30MHz can have a resistive component between 3 and 2000Ω, and a reactive component between -2500 and +500Ω. Gives criteria for achieving 1.2:1 SWR, i.e., 45 ≤ R ≤ 56Ω, 17.5 ≤ G ≤ 22.5 mS, -7° ≤ &phu; ≤ +7°. [10] "Antenna Tuner With a New Twist", Bob Baird W7CSD, Ham Radio June 1990, p59 & 61. Uses tapped coil and interpolation capacitor. Unusual use of L-C-L T-network configuration with mutual inductance between the coils. [11] The metal enclosure of a matching network forms a shorted turn around the inductor. Hence the eddy current losses in the case appear as a resistive component in the impedance of the coil. Lowest losses are incurred by using a large box, or failing that, a box made from material having high RF conductivity. Ferromagnetic materials having high resistivity (such as steel) are unsuitable. Silver-plated brass or plain copper may be too expensive for commercial designs, but aluminium is affordable and acceptable. Resistance at the joints between chassis and removable cover should be kept to a minimum by securing bare metal to bare metal at all overlap points, using plenty of screws. [12] It is sometimes argued that since the (unloaded) Q of a roller inductor increases as the inductance is increased, it is best to use the largest possible inductance. This is true when the inductance is in parallel with the the signal path, but not when it is in series. The unloaded Q of the coil does not dictate the efficiency of the system. What matters in this case is the series resistance, and this increases as the length of the conduction path through the inductor is increased. [13] "Clean Up Your Signals with Band-Pass Filters" Ed Wetherhold W3NQN, QST May 1998 p44-48, June 1998 p39-42. Three-resonator bandpass filters for 160, 80, 40, 20, 15, and 10m, using Micrometals (same as Amidon) powdered-iron and phenolic toroidal cores and high-voltage NPO ceramic capacitors (200W throughput, 50Ω termination). Design information and return loss measurements. Filters prevent radiation of spurious signals, and prevent receiver blocking and damage due to strong out-of-band signals (i.e., for multiple HF transceivers and antenna systems operating on the same site). [14] "A General-Purpose Antenna Matching Unit", M J Grierson, G3TSO. Rad Com, Jan 1987, p18-22. Reprinted in "HF Antenna Collection" Ed. David Erwin G4LQI, RSGB publ 1991 ISBN 1-872-309-089. p119-124. Constructional article describing T-match tuner with integral SWR meter and output-side balun. Author considers SPC and differential capacitor configurations but rejects them on grounds that harmonic suppression is provided by modern TX. Balun is voltage type 1:1 - 4:1 switched, with powdered iron toroidal core [for preference, see refs 1 - 4]. Suggested tuning procedure involves beginning with both capacitors set half-way. Observes "it is not uncommon ... for one capacitor to be very sharp ... while the other is flat and unresponsive". [15] "Understanding the T-tuner (C-L-C) Transmatch" William E Sabin, W0IYH, QEX, Dec. 1997, p13-21. Suggests that shorting out C1 and C2 will improve efficiency in some situations. States [incorrectly] that efficiency increases as L is reduced. [16] "Save Your Tuner for Two Pence", Tony Preedy, G3LNP, Rad Com, May 2000, p20-25. The "two pence" in question are copper cams used to make shorting switches for the capacitors in a commercial T-match tuner [note that defacing coins is illegal in many countries]. Article contains much useful information on ATU design and coil losses, with graphs of Q vs frequency for various roller inductors [unfortunately, working out which graph corresponds to which coil is left as a puzzle for the reader, but the solution appears to be a=1, b=2, e=5. If this is correct, graph e is for the inductor from an MFJ 989C tuner, and shows a Q of about 100 at 4MHz, and about 40 at 29MHz]. Author demonstrates that lowest losses occur in the T-match when one capacitor is set to its maximum value, and consequently gives correct procedure for adjustment. Goes on to describe shorting-switch modification, noting that in addition to reducing losses, it permits higher power on higher frequencies, and extends the upper frequency tuning limit for a given range of load impedances. In practice, notes that there is sometimes insufficient capacitance (in the commercial tuners modified) to effect a match with the L-configuration at lower frequencies, and the intermediate transformation (T-network) is required. [17] "The E-Z Tuner", James C Garland W8ZR, QST Apr 2002 p40-43. May 2002 p28-34, Jun 2002 p33-36. Reduces the number of coil tappings required for a T-network tuner on the basis of constant SWR curves and power loss curves [but considers only resistive loads in the design procedure]. [18] MFJ-986 Differential-T™ Antenna Tuner. Advertisement 2001. www.mfjenterprises.com . "Replacing two variable capacitors with a single differential capacitor gives a wide-range T-network tuner with only two controls. .. You get minimum SWR at only one setting and a broadband response that ends constant re-tuning". [19] "A differential T-match antenna tuner", Mike Grierson, G3TSO, Rad Com, Sept 1990, p48-49. Constructional article. The differential T-match is capable of matching a similar range of impedances to the traditional T-match. Efficiency is not discussed. [20] "The Ultimate Transmatch" Lew McCoy W1ICP, QST July 1970 p24-27, 58. The use of a roller inductor (as opposed to the then common amateur practice of using switched inductors) gives "almost unlimited" matching range. Uses 1:4 (Z) antenna-side balun. Claims efficiency of over 95% for mismatches up to 15:1 with an "adjustable dummy load" [resistor]. [21] "Ultimate Transmatch Improved" Doug DeMaw W1FB, Technical Correspondance, QST July 1980 p39. W1FB states [incorrectly, see 21a] that the original circuit was developed by the James Millen Co. and was popularised in QST by W1ICP as the "Ultimate" transmatch. Goes on to point out that the input-side parallel capacitor is redundant and the circuit is effectively an expensive T-match. The problem with the T-match is that under some circumstances it degenerates into a high-pass filter. Introduces the SPC circuit, which gives better harmonic attenuation and extends the low-frequency limit. [21a] "Set the Record Straight" Lew McCoy W1ICP, Correspondance, QST March 1981 p56. [22] "The Ultimate vs the SPC Transmatch", Walt Maxwell W2DU, Technical Correspondance, QST Aug 1981 p42-43. [23] "Ultimate vs SPC Transmatch" Tech Topics, Rad Com, Sept 1984, p771. G3KSU points out that the 'Ultimate' transmatch is still being advocated in books and journals, despite the shortcomings documented in the technical correspondance columns of QST in July 1980, March 1981, and August 1981. Essentially, the extra shunt capacitance across the TX terminals is useless and causes a reduction in efficiency. The drawback of the Ultimate was overcome by the 'SPC' (Series-Parallel Capacitance) configuration devised by Doug De Maw, W1FB, which offers improved harmonic attenuation [but reduced efficiency] compared to a straight T-network [the SPC configuration was also dropped by the ARRL Antenna Book by the 19th edition]. [24] "Which Transmatch?" Tony Smith G4FAI, Practical Wireless, Aug 1985, p22-23. G4FAI Modifies his 'Ultimate' to make it into an SPC. Also briefly discusses the history of the two networks: Lew McCoy W1ICP introduced the 'Ultimate' transmatch in a QST article in [July] 1961 [actually July 1970], several versions appeared in subsequent issues of the ARRL handbook, and commercial versions were produced. The SPC transmatch by Doug DeMaw W1FB appeared in the 1981 ARRL handbook. DeMaw had written to QST in July 1980 pointing out that the T-match would function as a HPF under some conditions, and a LPF between TX and transmatch was required. The SPC was developed in an effort to maintain a band-pass response under all load conditions. He claimed better harmonic attenuation and wider range compared to the 'Ultimate', and included details of tests carried out using a spectrum analyser. McCoy responded in March 1981 claiming that the extra 10dB of harmonic attenuation given by the 'Ultimate' was sufficient. In August 1981 [22], Walt Maxwell, W2DU, produced a detailed analysis of both circuits, observing that the input shunting capacitor of the 'Ultimate' was useless for impedance matching and reduced efficiency, but that the circuit did attenuate harmonics slightly. The harmonic attenuation of the SPC was substantially better. The 1983 ARRL handbook observed that harmonic attenuation with the 'Ultimate' can be as low as 3dB under some load conditions; whereas the SPC maintains a band-pass response with loads of <25 to >1000 Ω, this being due to the capacitance in parallel with the inductor. [25] "The ATU Debate Continues" Tech Topics, Rad Com, Dec 1984, p1055-6. "It would be a brave or foolhardy writer who claimed categorically that any one network was clearly superior to all others". Peter Chadwick, G3RZP, finds the SPC transmatch less eficient than a 4:1 transmission-line transformer and a series capacitor for matching an impedance of 12.5+j22Ω. The problem is that of excessive loaded Q. He prefers a parallel-tuned auto-transformer, adjusting the working Q by selecting the input and output taps and the L:C ratio, and canceling inductive reactance by means of a series capacitor in the output line. Admits that such tuners require elaborate switching and are not easy to set up. Discusses problem of arcing in un-shorted overwinds, and eddy currents in shorted overwinds. Rejects the idea of trying to get harmonic attenuation from an ATU, preferring the efficiency gain from operating the matching network with low working Q. Ivan James, G5IJ, favours the 'Ultimate' transmatch for voltage fed antennas, since the configuration reduces the required voltage rating of the ganged capacitors. Rejects the harmonic attenuation argument and recommends a multi-section LPF between the TX and the ATU. Also objects to the 1980 QST harmonic reduction tests, which used a 1000Ω test load for fundamental, 2nd, and 3rd harmonics, pointing out that the antenna impedance is hardly likely to be the same on all three frequencies. "the arguments about harmonic reduction depend so much on the actual antenna impedance that no definite conclusions can be drawn from such tests". Frank Rogers, G3BFR, converted a T-match to an SPC and found it extended the low-frequency limit. The Coil was 27μH, but C values are not given. Also, some material by Rob Gurr, VK5RG, on the Z-match, is reprinted. [26] "Estimating T-network losses at 80 and 160 meters", Kevin Schmidt, W9CF, QEX, July 1996 p16-20. Approximate formulae for estimating losses and peak intermediate voltages of T-network tuners on the basis of inductor Q. This approach indicates that the efficiencies of the basic T and the Ultimate are about the same. The differential T is about a factor of 2 worse than the basic network at low SWR, but becomes similar at high SWR. The SPC is always worse than the basic network, losses being increased by 50% for an SWR of 1, and doubled for low load resistance. Notes that L-networks are vastly more efficient at low frequencies when compared to T-networks with low maximum capacitance, but have reduced matching range. [27] "Getting the most out of your T-network antenna tuner", Andrew Griffith W4ULD, QST Jan 1995 p44-47. Loss is minimised by using the largest possible value for the antenna-side capacitor. [28] "How to evaluate your antenna tuner", Frank Witt AI1H, QST April 1995 p30-34, May 1995 p33-37. Loss estimation method using binary switched load resistors and an SWR meter. [29] The nominal power ratings of antenna tuners of North American origin are generally advertised to be twice the actual PEP rating. The idea is that the instantaneous DC input of a linear amplifier is about twice the PEP output (i.e., class AB amplifiers are about 50% efficient) and so the tuner power rating is the maximum DC input of the associated amplifier. This is a thoroughly silly system, and forces people to make qualfying statements such as: "The tuner is rated for 3KW DC input" (manual tuners do not have a DC input, except perhaps for the panel lamps). We should note, of course, that a tuner doesn't have a meaningful power rating on its own, it depends entirely on the antenna system. [30] Handbook of Lead-free Solder Techology for Microelectronic Assemblies, Karl J Puttlitz, Kathleen A Stalter, CRC Press, 2004. ISBN 0824748700, 9780824748708. Tin degradation phenomena, p925, p929. [31] The cleaning of silver is a job for the Butler, of course. Those unable to delegate can use Goddard's Silver Dip (S C Johnson Ltd), a sulphur sequestering agent. The component should be washed with copious running water after chemical cleaning, and should not be reinstalled untill completely dry. |
| Further Reading: |
|
The ARRL Antenna Book, 19th edition, ARRL publ,
2000. ISBN: 0-87259-804-7. Ch 25: Coupling the Transmitter to the Line. Discussion of harmonic attenuation in antenna tuners [pointing out that it is not reliable], and the problem with trapped antennas. Matching circuits: Inductive coupling, L-network, π-network, T-network. The 'Analyze Antenna Tuner' Program (supplied on CD-ROM with the book). Practical antenna tuners: Link-coupled, High-power T-network with input-side balun). CD ROM: AAT (Analyze antenna tuner program), etc. The ARRL Handbook 2000, 77th edition. ARRL publ. 1999, ISBN: 0-87259-183-2. Ch 13: RF Power Amplifiers Ch 22: Station Setup and Accessory Projects. High-Power T-match Antenna Tuner with TX-side balun, p56-59.) "Antenna matching", Tech Topics, Rad Com, Sept 1981, p818-819. Arthur collins, W0CXX, in the mid 1930s, popularised the 'Collins Universal Coupler' (π-network), on the basis that any TX could work successfully with any length of antenna. W2DK pointed out that when an antenna element presents to a transmission line an impedance other than R0, the impedance offered to the TX at the other end of the line may be quite different. The feeder acts as an impedance transformer. Unless a matching unit is interposed between the transmitter and the transmission line, the impedance may be of a value with which the TX output circuit cannot cope. An ATU must ideally cope with a very large range of impedances. Only one capacitor and one inductor is required to do this, but values and voltage ratings may become unwieldy. Most ATUs represent configurations aimed at reducing component sizes to manageable proportions. Dr M. J. Underhill, G3LHZ, presented a paper at a Leeds conference, showing that wide range matching can be achieved based on a two-stage approach, involving a pre-match unit (PMU) at the antenna junction, and a final-match unit (FMU) at the transceiver. The PMU may be, for example, a coaxial balun. An FMU design offering switchable π-network configurations to keep voltages within reasonable limits is given [see erratum, TT Nov 1981, next ref.]. The series variable capacitance and tapped inductor is suggested as an alternative to the roller-coaster coil. "Antenna matching for amateur bands", Tech Topics, Rad Com, Nov 1981, p1034. Variable capacitor marked 220pF in previous article should have been 2200pF. G3LHZ FMU circuit is reprinted with C1=1600pF (not 2200pF), since amateurs require only 1.8-30MHz, not 1.5-30MHz. "The transmitter / antenna Interface" Tech Topics, Rad Com, Dec 1984, p1054-5. Brief review of antenna coupling practices from early techniques onwards: The widespread introduction of VHF TV after the end of World War II brought about renewed interest in the π-network on accountof its low-pass characteristic. The need for better harmonic suppression however soon led to the fixed-impedance low-pass filter, which meant that transmitters were designed to work into a 50Ω load in order to terminate the LPF correctly. The output of the LPF was connected directly to the coax feedline of a resonant antenna. ATUs were relegated for use by those who used end-fed wires, open-wire feeders, or wanted extra harmonic suppression. The situation changed however with the introduction of solid-state transmitters with protection circuits, which do not give full output with high SWR. Few practical antennas provide sufficiently low SWR over entire amateur bands without the intervention of a matching unit. Consequently, the ATU came back into vogue. G3VA reminds us that a resonant antenna does not radiate any better than a non-resonant one. The new WARC bands make it necessary to be able to cope with a wide range of resistive and reactive load impedances. Repeats information on the G3LHZ PMU-FMU approach for those who did not see the 1981 articles (above). Also repeats circuit and information on the G3LHZ wide-range FMU. "The PA0SE Comudipole Multiband HF Antenna", Tech Topics, Rad Com, May 1993, p54-55. Dick Rollema, PA0SE, notes that it is not always convenient to bring the open-wire line into the transmitter room, and recommends a variation of the PMU-FMU scheme devised by Mike Underhill, G3LHZ (see "Antenna matching" TT sept. and Nov.1981, and "The Transmitter / Antenna Interface" Dec 1984, above). The G3LHZ information is repeated for those who did not see the 1981 and 1984 articles, giving construction details of a 4:1 air-cored coax balun (PMU) for connection via 50Ω coax (SWR <20:1) to a switch-configurable variable matching network (FMU). PA0SE considers the G3LHZ FMU over-complicated and adopts a simple switchabe L-network. Describes an installation with a 38m long inverted V dipole using 4:1 coax balun PMU at the antenna, 30m of RG213, and an L-network FMU. Perfect matching is obtained on 10 bands from 1.8 - 50MHz, but with low efficiency on 1.8MHz. Coax losses may be a few dB on some bands, "but this is a small price to pay for the convenience of a simple all band antenna without traps". The following statements, which appear in the article, are misleading : 1) "The advantage of [the coax] balun over those using ferrite or powdered iron toroids is that there is no danger of saturating the core [only imbalance currents can saturate the core, the fields from the differential-mode currents cancel] 2) "toroidal baluns are not really suitable with reactive loads" [the main problem is insufficient choking reactance when |Z| is large. Reactive loads increase losses, but the balun transmission line is short, and so the problem is not usually severe]. "PicATUne - the Intelligent ATU." Peter Rhodes, G3XJP, Rad Com, Sep 2000 p16-20, Oct 2000 p21-25, Nov 2000 p20-24, Dec 2000 p24-31, Jan 2001 p21-24 cont p29-30. Summary: Series of 5 articles describing an automatic ATU using only SWR and a search algorithm. L-match configuration with high Z - low Z switching is used on the basis of efficiency calculations. Efficiency graphs are given in part 1 (erratum part 4, p31). Design includes well-linearised tapped 30μH solenoid (graph in part 5 p24). Directional coupler is Sontheimer-Fredrick type 9 [US pat. 3426298 fig. 9, incorrectly attributed] used with dummy load on through port and antenna system on reverse port for quiet tuning (citing Underhill & Lewis, Electronic Letters, 4th Jan 1979). "Beyond the Z-Match. The IBZ coupler", Charles A Lofgrenn W6JJZ, Communications Quarterly, Winter (Jan) 1995 p27-32. "Appreciating the L Matching Network", Ernie Franke WA2EWT, Ham Radio, Sept 1980 p26-30. Theory and applications. "A Multiband Antenna System for the Newcomer" Lew McCoy W1ICP, QST, March 1959 p11-15. 3.5-30MHz balanced coupler using a double-tuned air-cored transformer. Selectable series or parallel tuned secondary. "A Wide-Range Transmatch" Lew McCoy W1ICP, QST, Nov 1961 p51-54 3.5-30MHz 500W coupler using a double-tuned air-cored transformer. Series tuned primary, capacitively tapped secondary. "A transmatch for Balanced and Unbalanced Lines" Lew McCoy W1ICP, QST, Oct 1966 p38-41. Use of the transmatch to provide selectivity, to prevent harmonic radiation and reduce receiver cross-modulation. 3.5-30MHz coupler using a double-tuned air-cored transformer. Series tuned primary, inductively tapped secondary. "Band-Switching Transmatches" Lance Johnson K1MET, QST 1967 p22-24. L-C-L T-network is used to match 50 Ohm unbalanced lines having SWR of less than 3:1. "Drake MN-4 Matching Network" W1DF, QST Oct 1967 p42-43. 3.5 - 30MHz Pi network with additional series capacitor. For matching coaxial lines with up to 5:1 SWR. |
|
"Graphical solution of impedance matching problems"
I L McNally W1NCK and Henry S Keen W2CTK, Ham Radio Dec 1969
p. Reprinted Mar 1978 p82-89. " ", Elmer Wingfield, W5FD, QST, Aug 1983, "A Note on Pi-L Networks" Elmer Wingfield, W5FD, QEX, Dec 1983 p5-9 "Analyzing Simple Matching Networks", Mark Bacon, KZ9J, QEX, Feb. 1987, p3-6, contd, p13. "Selectivity of Single-Resonator Coupling Networks", William E Sabin W0IYH, QEX July/Aug 2001 p43-47. "Impedance Matching: a brief review", Chris Bowick WD4C, Ham Radio, Jun 1984, p49-50, 53-56. Maximum power-transfer theorem. The conjugate match. Design of L-networks. "Examining the Mechancics of Wave Interference in Impedance Matching", Walter Maxwell W2DU, QEX Mar/Apr 1998, p17-24. "VSWR, Reflections, and the "Conjugate" Impedance Match", Dr Steven R Best VE9SRB, Communications Quarterly, Winter (Jan) 1999, p9-19. "Impedance Matching: Interpreting the Virtual Short Circuit", Dr Steven R Best VE9SRB [Cushcraft], Communications Quarterly, Fall (Oct) 1999, p31-56. The virtual short-circuit idea is wrong. Reflections from the input to the ATU are eliminated by a cancellation process. "Impedance Matching: Interpreting the Virtual Short Circuit (re: Communications Quarterly, Fall 1999): QEX (Letters to the Editor) Sept/Oct 2000, p60-62 Walter Maxwell W2DU. Dr Steven R Best VE9SRB. "Wave Mechanics of Transmission Lines, Part 1: Equivalence of Wave Reflection Analysis and the Transmission-Line Equation", Dr Steven R Best, VE9SRB, QEX Jan/Feb 2001, p3-8. "Wave Mechanics of Transmission Lines, Pt 2: Where Does Reflected Power Go", Dr Steven R Best, VE9SRB, QEX July/Aug 2001, p34-42. "Wave Mechanics of Transmission Lines, Part 3: Power Delivery and Impedance Matching", Dr Steven R Best, VE9SRB, QEX Nov/Dec 2001, p43-50. Correspondence, Lincoln Kraeuter KB1EYQ, QEX July/Aug 2002, p61. |
|
π-networks
for power amplifiers: "Pi-network design for high-frequency power amplifiers" Irvin M Hoff W6FFC, Ham Radio, Sept. 1972 . Reprinted June 1978 p52-64 "Pi Network Design and Analysis", Earl W Whyman W2HB, Ham Radio, Sept 1977, p30- "Pi Network Design", Leonard H Anderson, Ham Radio, March 1978 p36-40. π-networks for transmitter output stages. "Transmitter Matching Networks" Irvin M Hoff W6FFC, Ham Radio, March 1978 p42-46. Networks for matching an exciter to the input impedance of a linear amplifier. "Optimum pi-network design", Ulrich Fleischmann DL9LX, and Leonard H Anderson, Ham Radio Sept 1980, p50-56. Methods for optimising bandwidth without using the Q factor. Use of Z-plane diagram to illustrate the transformation process. "Pi-Network Formulas", Elmer Wingfield W5FD, (Correspondence) QEX Sept 1982, p2. Comments on defective p-network design formulae published in various amateur radio books and journals. "More on Pi-Network Formulas", Mason A Logan, K4MT, (Correspondence) QEX Dec 1982, p2. Corrections to the above. Series-parallel and parallel series transformations. "New and Improved Formulas for the Design of Pi and Pi-L Networks", Elmer A Wingfield W5FD, QST Aug 1983 p23- "Impedance Matching - A Brief Review", Chris Bowick W4DC, Ham Radio, June 1984, p48- Walt Maxwell W2DU, Technical Correspondence, QST, Mar 1985, p45-. "Design a toroidal tank circuit for your vacuum tube amplifier", Robert E Bloom W6YUY, Ham Radio, Aug 1985, p29-31, 33-36. Full design procedure for amplifiers up to 2KW. "Pi Network Capacitor Equations", Mason A Logan, K4MT, Ham Radio, Oct 1988, p109-110. "A Concise Calculation Method for Pi-L Networks", Karl Gerhard Lickfeld, DL3FM, QEX Sept/Oct 1998 p47-49. "A Concise Calculation Method for Pi-L Networks" William H Sayer WA6BAN, Doug Smith KF6DX (Editor), (Correspondence) QEX March/April 1999, p59-60. Errors in Lickfield's article. "A Concise Calculation Method for Pi-L Networks" Vince Bartell W0MFK (Correspondence) QEX, May/June 1999, p61. Lickfield's method is flawed. |
© D W Knight 2009.
|
|
|
|
|
|