シリーズ・リアクタンス・マッチングについて･･･ARRL HANDBOOKより(Sep 23. 2014)
プレート回路から50Ω負荷へマッチング(整合)をとる場合、HFでは集中定数(L･C)によるπマッチや並列共振直列給電(リンクコイル)方式が一般的だ。
しかし、144MHzや430MHz帯になるとこの方法ではプレート出力CやストレーC及びストレーLが効き、目的周波数で一定の負荷抵抗値を確保した共振を得るのは困難に等しい。
そこで線路長(電気長λ/4･�?2)を利用した共振回路を、プレート出力CやストレーCを含めて構成する方法が採用されるようになった。
そして、微小Cによるプレート同調と、同様に微小Cによるプレートからの負荷結合を行う手法が併用されている。
ARRL HANDBOOKには古くからその解説が行われていたが、最新の2014年版を見るとその記述が無くなっている。
いまさら真空管なんて･･･とする声が聞こえてきそうだが、整合を理解するためのテクニックの一つとして知っておいて損は無い。
ポイントはC･R(50Ω)の直列回路を並列回路に等価変換して取り扱う処にある。Z=R±Xの直列回路のみに拘っているとこの「シリーズ･リアクタンス･マッチング」の理解には辿りつけない。
以下にARRL HANDBOOK 2006のChapter 18からの抜粋をまとめてみた。ここでは144MHzを例に説明している。
参考情報：Daycounter,Incのサイトに直列-並列変換カリキュレータがあるので便利だ。例えば直列Cと50Ωの直列回路のインピーダンスが145MHzで等価になる並列回路の定数を瞬時に計算してくれる。
なお、当然ながら並列回路でも-jX成分が存在するので、これはプレート同調Cや線路長等との兼ね合いでキャンセルすることになる。
同社のサイトにはその他便利なカリキュレータの案内が多数あるので有効利用すると良い。
スミスチャートソフトでRs-jXsをプロットしてから表示をアドミッタンスチャートに切替え、その表示値からRpとXpを読み定数を計算する方法もあるが、このカリキュレータを使えば一瞬にしその作業が行え、微調整も瞬時にして行える。
From THE ARRL HANDBOOK 2006 Chapter 18 “RF Power Amplifires”
TANK OUTPUT CIRCUITS
Tank circuit output networks need not take the form of a capacitor connected in parallel with an inductor. A number of equivalent circuits can be used to match the impedances normally encountered in a power amplifier. Most are operationally more flexible than a parallel-resonant tank. Each has its advantages and disadvantages for specific applications, but the final choice usually is based on practical construction considerations and the component values needed to implement a particular network. Some networks may
require unreasonably high or low inductance or capacitance values. In that case, use another network, or a different value of QL. Several different networks may be investigated before an acceptable final design is reached.
The impedances of RF components and amplifying devices frequently are given in terms of a parallel combination of a resistance and a reactance, although it is often easier to use a series R-X combination
to design networks. Fortunately, there is a series impedance equivalent to every parallel impedance and vice versa. The equivalent circuits, and equations for conversion from one to the other, are given in
Fig 18.4. In order to use most readily available design equations for computing matching networks, the parallel impedance must first be converted to its equivalent series form.
The QL of a parallel impedance can be derived from the series form as well. Substitution of the usual formula for calculating QL into the equations from Fig 18.4 gives
QL = Rp/Xp (12)
where
Rp = the parallel equivalent resistance
Xp = the parallel equivalent reactance
DESIGN EXAMPLE 2 : A MEDIUM POWER 144MHz AMPLIFIER
For decades the 4CX250 family of power tetrodes has been used successfully up through 500 MHz. They are relatively inexpensive, produce high gain and lend themselves to relatively simple amplifier designs. In amateur service at VHF, the 4CX250 is an attractive choice for an amplifier. Most VHF exciters used now
by amateurs are solid state and often develop 10 W or less output. The drive requirement for the 4CX250 in grounded cathode, Class AB operation ranges between 2 and 8 W for full power output, depending on frequency. At 144 MHz, manufacturer’s specifications suggest an available output power of over 300 W.
This is clearly a substantial improvement over 10 W, so a 4CX250B will be used in this amplifier.
The first design step is the same as in the previous example: Verify that the proposed tube will perform as desired while staying within the manufacturer’s ratings.
Again assuming a basic amplifier efficiency of 60% for Class AB operation, 300 W of output requires a plate input power of 500 W. Tube dissipation is rated at 250 W, so plate dissipation is not a problem,
as the tube will only be dissipating 200 W in this amplifier. If the recommended maximum plate potential of
2000 V is used, the plate current for 500 W input will be 250 mA, which is within the manufacturer’s ratings. The plate load resistance can now be calculated. Using the same formula as before, the value is determinedto be 5333Ω.
The next step is to investigate the output circuit. The manufacturer’s specification for COUT is 4.7 pF. The inevitable circuit strays along with the tuning capacitor add to the circuit capacitance. A carefully built amplifier might only have 7 pF of stray capacitance, and a specially made tuning capacitor can be fabricated to have a midrange value of 3 pF. The total circuit capacitance adds up to about 15 pF.
At 144 MHz this represents a capacitive reactance of only 74Ω. The QL of a tankcircuit with this reactance with a plate load resistance of 5333Ω?is 5333/74 = 72. A pi output matching network would be totally impractical, because the L required would be extremely small and circuit losses would be prohibitive. The simplest solution is to connect an inductor in parallel with the circuit capacitance to form a parallel-resonant tank circuit.
To keep tank circuit losses low with such a high QL, an inductor with very high unloaded Q must be used. The lowest-loss inductors are formed from transmissionline sections. These can take the form of either coaxial lines or strip lines. Both have their advantages and disadvantages, but the strip line is so much easier to fabricate that it is almost exclusively used in VHF tank circuits today.
The reactance of a terminated transmission line section is a function of both its characteristic impedance and its length (see the Transmission Lines chapter).
The reactance of a line terminated in a short circuit is
Xin = Zo tan l (46)
where
Xin = is the circuit reactance.
Zo = the line’s characteristic impedance
l = the transmission line length in degrees
For lines shorter than a quarter wavelength (90°) the circuit reactance is inductive. In order to resonate with the tank-circuit capacitive reactance, the transmission-line reactance must be the same value, but inductive. Examination of the formula for transmission-line circuit reactance suggests that a wide range of lengths can yield the same inductive reactance, so long as the line Zo is appropriately scaled. Based on circuit Q considerations, the best bandwidth for a tank circuit results when the ratio of Zo to XIN is between one and two. This implies that transmission line lengths between 26.5°and 45°give the best bandwidth. Between these two limits, and with some adjustment of Zo, practical transmission lines can be designed. A transmission-line length of 35° is 8 inches long at 144 MHz, a workable dimension mechanically. Substitution of this value into the transmission-line equation gives a Zo of 105Ω.
The width of the strip line and its placement relative to the ground planes determine the line impedance. Other stray capacitances such as mounting standoffs also affect the impedance. Accurate calculation
of the line impedance for most physical configurations requires extensive application of Maxwell’s equations and is beyond the scope of this book. The specialized case in which the strip line is parallel to and located halfway between two ground planes has been documented in Reference Data for Radio Engineers (see Bibliography). According to charts presented in that book, a 105-Ω?strip line impedance is obtained by placing a line with a width of approximately 0.4 times the ground plane separation halfway between the ground planes. Assuming the use of a standard 3-inch-deep chassis for the plate compartment, this yields a stripline width of 1.2 inches. A strip line 1.2 inches wide located 1.5 inches above the chassis floor and grounded at one end has an inductive reactance of 74Ω?at 144 MHz.
The resulting amplifier schematic diagram is shown in Fig 18.18. L2 is the stripline inductance just described. C3 is the tuning capacitor, made from two parallel brass plates whose spacing is adjustable.
One plate is connected directly to the strip line while the other is connected to ground through a wide, low-inductance strap. C2 is the plate blocking capacitor. This can be either a ceramic doorknob capacitor such as the Centralab 850 series or a homemade “Teflon sandwich.” Both are equally effective at 144 MHz.
Impedance matching from the plate resistance down to 50Ω?can be either through an inductive link or through capacitive reactance matching. Mechanically, the capacitive approach is simpler to implement. Fig 18.19 shows the development of reactance matching through a series capacitor (C4 in Fig 18.19). By
using the parallel equivalent of the capacitor in series with the 50Ω?load, the load resistance can be transformed to the 5333Ω?plate resistance. Substitution of the known values into the parallel-toseries
equivalence formulas reveals that a 2.15 pF capacitor at C4 matches the 50Ω load to the plate resistance. The resulting parallel equivalent for the load is 5333Ω in parallel with 2.13 pF. The 2.13-pF
capacitor is effectively in parallel with the tank circuit.
A new plate line length must now be calculated to allow for the additional capacitance. The equivalent circuit diagram containing all the various reactances is shown in Fig 18.20. The total circuit capacitance is now just over 17 pF, which is a reactance of 64Ω. Keeping the stripline width and thus its impedance constant at 105Ω?dictates a new resonant line length of 31°. This calculates to be 7.14 inches for 144 MHz.
The alternative coupling scheme is through the use of an inductive link. The link can be either tuned or untuned. The length of the link can be estimated based on the amplifier output impedance, in this case, 50Ω. For an untuned link, the inductive reactance of the link itself should be approximately equal to the output impedance, 50Ω. For a tuned link, the length depends on the link loaded Q, QL. The link QL should generally be greater than two, but usually less than five. For a QL of three this implies a capacitive reactance of 150Ω, which at 144 MHz is just over 7 pF.
The self-inductance of the link should of course be such that its impedance at 144 MHz is 150Ω?(0.166 mH). Adjustment of the link placement determines the transformation ratio of the circuit line. Some fine adjustment of this parameter can be made through adjustment of the link series tuning capacitor. Placement of the link relative to the plate inductor is an empirical process.
The input circuit is shown in Figs 18.21 and 18.23. CIN is specified to be 18.5 pF for the 4CX250. This is only ?j 60Ω?at 2 m, so the pi network again is unsuitable.
Since a surplus of drive is available with a 10 W exciter, circuit losses at the amplifier input are not as important as at the output.
An old-fashioned “split-stator” tuned input can be used. L1 in Fig 18.18 is series tuned by CIN and C1. The two capacitors are effectively in series (through the ground return). A 20-pF variable at C1 set to
18.5 pF gives an effective circuit capacitance of 9.25 pF. This will resonate at 144 MHz with an inductance of 0.13 ?H at L1. L1 can be wound on a toroid core for mechanical convenience. The 50Ω?input impedance is then matched by link coupling to the toroid. The grid impedance isprimarily determined by the value for R1, the grid bias feed resistor.
