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投稿者 スレッド
webadm
投稿日時: 2008-6-18 22:06
Webmaster
登録日: 2004-11-7
居住地:
投稿: 2943
Re: VFO
取説にはVFOの調整方法が書いてあるものの、インダクタのコアを回すのとトリマーコンデンサーを回すのを交互に繰り返して最終的に上限と下限が目的の値になるようにするというもの。

一度回してしまうと後戻りが出来ないので、試行錯誤しないでぴったり調整する方法はないものかと思案。

VFOはいずれもLC共振回路を利用したトランジスタ一石のコルピッツもしくはハートレー発振回路と呼ばれるもの。



本来は発振回路を解析して目的の周波数範囲を出力できるような定数を割り出すことができればいいのだけれども、そんな知識も技術があるわけもなく。

それでも電気回路理論おもちゃ箱で学んだ共振回路の理論を応用してなにかできないか考えてみた。発振回路のLC共振回路部分は反固定のインダクタと固定+反固定のキャパシタそれにバリコンで構成されている。現在の発振周波数上限と下限からこのLC回路の定数を割り出すことができるはずである。LC共振回路の共振周波数は

f0=1/(2π√(L*C))

で表される。共振周波数の上限はバリコンを一杯に抜いたとき(0pF)の時で、下限はバリコンが一杯に入った時(60pF)とすればそれぞれの共振周波数に関して以下の2つの式が成り立つ

f0max=1/(2π√(L*C))
f0min=1/(2π√(L*(C+60*10^-12)))

これをLとCに関する二元連立方程式として解けば与えられたf0maxとf0minに対する適切なLとCの値を求めることができる。

Maximaで解くには両辺を二乗して一次以上の式にする必要がある。

f0max^2=1/((2π)^2*(L*C))
f0min^2=1/((2π)^2*(L*(C+60*10^-12)))

(%i1) e1: f0max^2=1/((2*%pi)^2*(L*C));
(%o1) f0max^2=1/(4*%pi^2*C*L)
(%i2) e2: f0min^2=1/((2*%pi)^2*(L*(C+60*10^-12)));
(%o2) f0min^2=1/(4*%pi^2*(C+3/50000000000)*L)
(%i3) solve([e1,e2],[L,C]);
(%o3) [[L=-(12500000000*f0min^2-12500000000*f0max^2)/(3*%pi^2*f0max^2*f0min^2),C=-(3*f0min^2)/(50000000000*f0min^2-50000000000*f0max^2)]]

これに現在のf0maxとf0minの実測値を代入すると

(%i7)
subst(85.0*10^6, f0max, [[L=-(12500000000*f0min^2-12500000000*f0max^2)/(3*%pi^2*f0max^2*f0min^2),C=
-(3*f0min^2)/(50000000000*f0min^2-50000000000*f0max^2)]]);
(%o7) [[L=(4.6136101499423294*10^-17*(9.0312499999999996*10^+25-12500000000*f0min^2))/(%pi^2*f0min^2),C=-
(3*f0min^2)/(50000000000*f0min^2-3.6124999999999999*10^+26)]]
(%i8)
subst(54.2*10^6, f0min, [[L=(4.6136101499423294*10^-17*(9.0312499999999996*10^+25
-12500000000*f0min^2))/(%pi^2*f0min^2),C=-(3*f0min^2)/(50000000000*f0min^2-3.6124999999999999*10^
+26)]]);
(%o8) [[L=(8.4167084855771767*10^-7)/%pi^2,C=4.1111173309449178*10^-11]]
(%i9) float(%), numer;
(%o9) [[L=8.5279086613118777*10^-8,C=4.1111173309449178*10^-11]]

L=85.2 [nH]
C=41.1 [pF]

ということになる。

次ぎに本来のf0maxとf0minにするためにLとCをいくつにすればよいか求めてみる。f0max=85.2MHz,f0min=54.0MHzを代入してみると

(%i10)
subst(85.2*10^6, f0max, [[L=-(12500000000*f0min^2-12500000000*f0max^2)/(3*%pi^2*f0max^2*f0min^2),C=
-(3*f0min^2)/(50000000000*f0min^2-50000000000*f0max^2)]]);
(%o10) [[L=(4.5919754310946532*10^-17*(9.0738000000000007*10^+25-12500000000*f0min^2))/(%pi^2*f0min^2),C=-
(3*f0min^2)/(50000000000*f0min^2-3.6295200000000003*10^+26)]]
(%i11)
subst(54.0*10^6, f0min, [[L=(4.5919754310946532*10^-17*(9.0738000000000007*10^+25
-12500000000*f0min^2))/(%pi^2*f0min^2),C=-(3*f0min^2)/(50000000000*f0min^2-3.6295200000000003*10^
+26)]]);
(%o11) [[L=(8.5490110494947379*10^-7)/%pi^2,C=4.0285145888594158*10^-11]]
(%i12) float(%), numer;
(%o12) [[L=8.6619591850623112*10^-8,C=4.0285145888594158*10^-11]]

L=86.6 [nH]
C=40.3 [pF]

ということでLを若干増してCを若干減らす必要がある。同時にそれを行うのは難しいので、まず片方を目的の値にした場合にf0max,f0minがどうなるか計算してみよう。

最初のf0maxとf0minの式にLは現状のままでCを変更した場合を計算してみると

(%i13) f0max=1/((2*%pi)*sqrt(L*C));
(%o13) f0max=1/(2*%pi*sqrt(C*L))
(%i14) f0min=1/((2*%pi)*sqrt(L*(C+60*10^-12)));
(%o14) f0min=1/(2*%pi*sqrt((C+3/50000000000)*L))

(%i21) subst(85.2*10^-9, L, f0max=1/(2*%pi*sqrt(C*L)));
(%o21) f0max=1712.971774568829/(%pi*sqrt(C))
(%i22) subst(40.3*10^-12, C, f0max=1712.971774568829/(%pi*sqrt(C)));
(%o22) f0max=(2.698346290949257*10^+8)/%pi
(%i23) float(%), numer;
(%o23) f0max=8.5891030075651169*10^+7

f0max'=85.9 [MHz]

(%o24) f0min=1712.971774568829/(%pi*sqrt(C+3/50000000000))
(%i25) subst(40.3*10^-12, C, f0min=1712.971774568829/(%pi*sqrt(C+3/50000000000)));
(%o25) f0min=(1.7104080837713531*10^+8)/%pi
(%i26) float(%), numer;
(%o26) f0min=5.4443980247309491*10^+7

f0min'=54.4 [MHz]

とすこし高い方へシフトする。最初にトリマーコンデンサを回してこの周波数になるように前調整した上でインダクタのコアを回して目的の上限と下限になるようにすれば最短で調整ができることになる。

同様にVFO Bについてはバリコンが335pFの容量なので同様に現状の定数を割り出すと

(%i1) e1: f0max^2=1/((2*%pi)^2*(L*C));
(%o1) f0max^2=1/(4*%pi^2*C*L)
(%i27) e2: f0min^2=1/((2*%pi)^2*(L*(C+335*10^-12)));
(%o27) f0min^2=1/(4*%pi^2*(C+67/200000000000)*L)
(%i28) solve([e1,e2],[L,C]);
(%o28) [[L=-(50000000000*f0min^2-50000000000*f0max^2)/(67*%pi^2*f0max^2*f0min^2),C=-(67*f0min^2)/(200000000000*f0min^2-200000000000*f0max^2)]]

(%i29)
subst(3.478*10^6, f0max, [[L=-(50000000000*f0min^2-50000000000*f0max^2)/(67*%pi^2*f0max^2*f0min^2),C=
-(67*f0min^2)/(200000000000*f0min^2-200000000000*f0max^2)]]);
(%o29) [[L=(1.2338604452606529*10^-15*(6.0482419999999976*10^+23-50000000000*f0min^2))/(%pi^2*f0min^2),C=-
(67*f0min^2)/(200000000000*f0min^2-2.419296799999999*10^+24)]]
(%i30)
subst(2.941*10^6, f0min, [[L=(1.2338604452606529*10^-15*(6.0482419999999976*10^+23
-50000000000*f0min^2))/(%pi^2*f0min^2),C=-(67*f0min^2)/(200000000000*f0min^2-2.419296799999999*10^
+24)]]);
(%o30) [[L=(2.458598762396727*10^-5)/%pi^2,C=8.4060737254943044*10^-10]]
(%i31) float(%), numer;
(%o31) [[L=2.4910813670762317*10^-6,C=8.4060737254943044*10^-10]]

L=2.49 [uH]
C=840 [pF]

ということになる。

f0max=3.48MHz,f0min=2.38MHzとするには同様に

(%i32)
subst(3.48*10^6, f0max, [[L=-(50000000000*f0min^2-50000000000*f0max^2)/(67*%pi^2*f0max^2*f0min^2),C=
-(67*f0min^2)/(200000000000*f0min^2-200000000000*f0max^2)]]);
(%o32) [[L=(1.2324426224012716*10^-15*(6.0551999999999995*10^+23-50000000000*f0min^2))/(%pi^2*f0min^2),C=-
(67*f0min^2)/(200000000000*f0min^2-2.4220799999999998*10^+24)]]
(%i33)
subst(2.38*10^6, f0min, [[L=(1.2324426224012716*10^-15*(6.0551999999999995*10^+23
-50000000000*f0min^2))/(%pi^2*f0min^2),C=-(67*f0min^2)/(200000000000*f0min^2-2.4220799999999998*10^
+24)]]);
(%o33) [[L=(7.0125036579325205*10^-5)/%pi^2,C=2.9438008067018309*10^-10]]
(%i34) float(%), numer;
(%o34) [[L=7.1051517091794628*10^-6,C=2.9438008067018309*10^-10]]

L=7.1 [uH]
C=294 [pF]

という具合にLを3倍に増やしてCを3分の1ぐらいに減らす必要がある。しかし回路図を見ると可変できるトリマーコンデンサの容量は20pFしかない。これでは調整不能である。何か周辺がおかしいとしか言いようが無い。実際の基板を良く調査する必要がありそうだ。

ちなにみCを現状のままでLを最終的な値に調整した時のf0max,f0minを計算すると

(%i38) subst(7.1*10^-6, L, f0max=1/(2*%pi*sqrt(C*L)));
(%o38) f0max=187.6466562602004/(%pi*sqrt(C))
(%i39) subst(840*10^-12, C, f0max=187.6466562602004/(%pi*sqrt(C)));
(%o39) f0max=(938.233281301002*10^(9/2))/(sqrt(21)*%pi)
(%i40) float(%), numer;
(%o40) f0max=2060873.40226868

f0max'=2.06 [MHz]

(%i42) subst(7.1*10^-6, L, f0min=1/(2*%pi*sqrt((C+67/200000000000)*L)));
(%o42) f0min=187.6466562602004/(%pi*sqrt(C+67/200000000000))
(%i43) subst(840*10^-12, C, f0min=187.6466562602004/(%pi*sqrt(C+67/200000000000)));
(%o43) f0min=(3.7529331252040081*10^+7)/(sqrt(47)*%pi)
(%i44) float(%), numer;
(%o44) f0min=1742496.939488731

f0min'=1.74 [MHz]

ということになる。ここまで調整できたらトリマーコンデンサーを回して最終的な目標値になるようにすればいいはずだが、果たしてできるのかどうか疑問。

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                                                                                                           Radio NewZealand webadm 2008-10-19 17:21
                                                                                                             ラジオタイランド webadm 2008-11-2 22:29
                                                                                                               そろそろ室外ループアンテナが webadm 2008-11-3 1:47
                                                                                                                 京劇放送が停波した背景 webadm 2008-11-8 21:49
                                                                                                                   中国のエンタメ webadm 2008-11-10 1:44
                                                                                                                     ここ数日の7MHz帯 webadm 2008-11-17 21:28
                                                                                                                       最近の受信機オークション webadm 2008-11-19 22:51
                                                                                                                       Re: ここ数日の7MHz帯 webadm 2008-12-19 21:39
                                                                                                                         Re: ここ数日の7MHz帯 webadm 2008-12-21 17:19
                                                                                                                           Re: ここ数日の7MHz帯 webadm 2008-12-24 9:49
                                                                                                                             Re: ここ数日の7MHz帯 webadm 2008-12-26 14:08
                                                                                                                               Re: ここ数日の7MHz帯 webadm 2008-12-27 12:29
                                                                                                                                 Re: ここ数日の7MHz帯 webadm 2009-1-17 14:09
                                                                                                                                   Re: ここ数日の7MHz帯 webadm 2009-2-5 23:28
                                                                                                                                     7100〜7200kHz拡張 webadm 2009-4-1 4:53
                                                                                                                                       ワッチは継続中 webadm 2010-1-19 15:53
                                                                                                                                         Re: ワッチは継続中 webadm 2010-7-15 17:35
                                                                                                                                           夏の9MHz帯 webadm 2010-7-26 19:33
                                                                                                                                             夏の11MHz帯 webadm 2010-8-16 22:05
                                                                                                                                               Re: 夏の11MHz帯 webadm 2010-8-24 23:48
                                                                                                                                                 もはや平壌放送ワッチ webadm 2010-8-31 21:40
                                                                                                                                                   Re: もはや平壌放送ワッチ webadm 2010-9-16 1:39
                                                                                                                                                     Re: もはや平壌放送ワッチ webadm 2010-9-26 21:44
                                                                                                                                                       Re: もはや平壌放送ワッチ webadm 2010-10-16 0:59
                                                                                                                                                         Re: もはや平壌放送ワッチ webadm 2010-10-23 11:17
                                                                                                                                                           Re: もはや平壌放送ワッチ webadm 2010-10-28 0:40
                                                                                                                                                             日本の声 webadm 2010-11-13 19:10
                                                                                                                                                               Re: 日本の声 webadm 2010-11-15 10:16
                                                                                                                                                                 FRG-7000故障 webadm 2010-11-21 12:07
                                                                                                                                                                   KBS World Radio webadm 2010-11-21 12:23
                                                                                                                                                                     京劇放送復活? webadm 2010-11-21 12:33
                                                                                                                                                                       平壌放送愛好会 webadm 2010-11-22 16:45
                                                                                                                                                                         Re: 平壌放送愛好会 webadm 2010-11-24 13:53
                                                                                                                                                                           北朝鮮砲撃報道 webadm 2010-11-26 7:17
                                                                                                                                                                             Re: 北朝鮮砲撃報道 webadm 2010-11-28 3:15
                                                                                                                                                                               Re: 北朝鮮砲撃報道 webadm 2010-11-29 14:43
                                                                                                                                                                                 Re: 北朝鮮砲撃報道 webadm 2010-11-30 9:34
                                                                                                                                                                                   Re: 北朝鮮砲撃報道 webadm 2010-12-2 21:13
                                                                                                                                                                                     Re: 北朝鮮砲撃報道 webadm 2010-12-3 12:55
                                                                                                                                                                                       各国の国際放送のwebページ webadm 2010-12-6 13:55
                                                                                                                                                                                         送信機の状態が悪そう webadm 2010-12-8 18:17
                                                                                                                                                                                           Re: 送信機の状態が悪そう webadm 2010-12-9 12:55
                                                                                                                                                                   Re: FRG-7000故障 webadm 2010-11-23 8:22
                                                                                                                                                                     Re: FRG-7000故障 webadm 2010-11-24 13:22
                                                                                                                                                                       Re: FRG-7000故障 webadm 2010-11-26 12:51
                                                                                                                                                                         Re: FRG-7000故障 webadm 2010-11-26 14:23
                                                                                                                                                                           Re: FRG-7000故障 webadm 2010-11-28 2:32
                                                                                                                                                                       Re: FRG-7000故障 webadm 2010-12-2 21:25
                                   Re: ノイズフィルター webadm 2008-9-6 20:12
     FRG-965/9600入手 webadm 2010-12-26 13:17
       Re: FRG-965/9600入手 webadm 2010-12-26 15:09
         Re: FRG-965/9600入手 webadm 2010-12-27 23:57
           FRG-965/9600故障 webadm 2011-10-15 3:29
             Re: FRG-965/9600故障 webadm 2011-10-15 15:37
             Re: FRG-965/9600故障 webadm 2011-10-16 15:03

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