臨床工学技士国家試験・ME2種増幅器まとめ

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June 15, 22

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臨床工学技士国家試験・ME2種で出題されるオペアンプなどの増幅器に関する内容をまとめた資料です.公立小松大学臨床工学科の学生向けの資料ですが,皆さんのお役に立てると幸いです.

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臨床⼯学技⼠国家試験・ ME2種 増幅器まとめ 藤⽥ ⼀寿

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抑えるポイント • デシベル𝐺 = 20 log!" #! #" • 多段増幅器の利得は,各増幅器の利得(dB)を⾜す. • オペアンプ • ⼊⼒インピーダンスは無限⼤.⼊⼒には電流は⼊っていかない. • イマジナリショート.⼊⼒端⼦同⼠は仮想的な短絡状態である. • ⼊⼒端⼦同⼠は同じ電位である. • オペアンプの問題は上の2点を使えば解ける. • 差動増幅度𝐴$ と同相増幅度𝐴% の⽐を同相除去⽐CMRRという. # • 𝐶𝑀𝑅𝑅 = 20 log!" #! = 20 log!" 𝐴$ − 20 log!" 𝐴% [dB] "

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増幅度,利得

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増幅 • ⼊⼒信号の振幅を⼤きくした出⼒を得ることを増幅という. • ⼩さい波を⼤きい波にする. • 増幅に⽤いられる増幅回路という. • 増幅回路を持った機器を増幅器という. 増幅器により大きくなった信号 声 増幅器 小さな信号

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増幅度,利得(ゲイン) • ⼊⼒がどれほど増幅されたかを,増幅度,利得(ゲイン)で表す. vo Av = • 電圧増幅度 vi Gv = 20 log10 |Av | • 電圧利得 <latexit sha1_base64="kKVrKVkpjCf+HafVdjNs0a+mKlA=">AAACDHicbVDLSgMxFM3UV62vqks3wSK4KjNS1I1QHwuXFewDOsOQSTNtaCYZkkyhDPMBbvwVNy4UcesHuPNvTNsBtfVA4HDOudzcE8SMKm3bX1ZhaXllda24XtrY3NreKe/utZRIJCZNLJiQnQApwignTU01I51YEhQFjLSD4fXEb4+IVFTwez2OiRehPqchxUgbyS9XLv0RvIBuKBFO3RvCNIIjX2Q/nGYmZVftKeAicXJSATkafvnT7QmcRIRrzJBSXceOtZciqSlmJCu5iSIxwkPUJ11DOYqI8tLpMRk8MkoPhkKaxzWcqr8nUhQpNY4Ck4yQHqh5byL+53UTHZ57KeVxognHs0VhwqAWcNIM7FFJsGZjQxCW1PwV4gEyvWjTX8mU4MyfvEhaJ1XntFq7q1XqV3kdRXAADsExcMAZqINb0ABNgMEDeAIv4NV6tJ6tN+t9Fi1Y+cw++APr4xvJR5rb</latexit> <latexit sha1_base64="OUAittTjxgAZwwwDOnl0IRNRsDs=">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</latexit> [dB] デシベル io ii vi 入力端子 増幅度と利得は同じ意味 で同じように使う場合も あれば,デシベル表示の み利得という場合もある .文脈で判断してほしい . 増幅回路 vo 出力端子

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対数の計算 • 利得の計算をするためには対数の計算を習得する必要がある.次の公 式を思い出そう. • aを底とし,M>0,N>0とする. loga 1 = 0 <latexit sha1_base64="Lpl4xTVpkbLLriKpjjAg0I14YZs=">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</latexit> loga a = 1 loga (M N ) = loga M + loga N loga (M/N ) = loga M loga M r = r loga M loga N

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多段増幅回路 • 増幅回路を複数つなげ回路を多段増幅回路という. • 多段増幅回路の電圧増幅度Aは各増幅回路の増幅度を書けたものになる. • 𝐴 = 𝐴! 𝐴& ⋯ • 多段増幅回路Gの電圧利得は次のように計算できる. • 𝐺 = 20 log!" 𝐴 = 20 log!" 𝐴! 𝐴& ⋯ = 20 log!" 𝐴! + 20 log!" 𝐴& + ⋯ • = 𝐺! + 𝐺& + ⋯ • つまり多段増幅回路の利得は各増幅回路の利得を⾜したものになる. 増幅回路2 増幅回路1 入力 増幅度A1 A1倍 増幅度A2 A1A2倍

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第39回ME2種 • 図のような電圧増幅器を内蔵する医療機器に1mVを⼊⼒したときの出 ⼒の振幅[V]はどれか 1. 0.02 2. 0.04 3. 0.1 4. 0.3 5. 10

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第39回ME2種 • 図のような電圧増幅器を内蔵する医療機器に1mVを⼊⼒したときの出 ⼒の振幅[V]はどれか 1. 0.02 2. 0.04 3. 0.1 4. 0.3 5. 10 多段増幅回路の利得は各増幅回路の利得を足し合わせたものなので,多段増幅回路の利得は, 30+10=40dB よって増幅度は 20 log!" 𝐴 = 40 𝐴 = 100 よって,この多段増幅回路は入力電圧を100倍にするので,出力は100mV=0.1Vとなる.

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第35回ME2種 • 図の回路の電圧増幅度は全体でいくらか. 1. 2倍 2. 40倍 3. 100倍 4. 399倍 5. 10000倍

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第35回ME2種 • 図の回路の電圧増幅度は全体でいくらか. 1. 2倍 2. 40倍 3. 100倍 4. 399倍 5. 10000倍 多段増幅回路の利得は各増幅回路の利得を足し合わせたものなので,多段増幅回路の利得は, 19+21=40dB よって増幅度は 20 log!" 𝐴 = 40 𝐴 = 100 よって,この多段増幅回路は入力電圧を100倍にする. テクニック:暗算で計算できる増幅度は10の倍数以外ありえないので答えは3か5に絞られる.

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オペアンプ

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オペアンプ • 演算増幅器 (Operation Amplifier: オペアンプ) • 反転⼊⼒と⾮反転⼊⼒の2つの⼊⼒端⼦がある. • 正負直流電源を使う. • 出⼒が1つある. • オペアンプの応⽤例 • 増幅回路 • ⾮反転増幅回路 • 反転増幅回路 • バッファ回路 反転入力 - • ボルテージフォロア • 加算回路,減算回路 • コンパレータ + 非反転入力 出力

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理想オペアンプ • 増幅度は無限⼤ • いくらでも増幅できる. • 2つの入力端子の入力インピーダンスが無限大 重要!! • 入力端子に電流は入っていかない. • 出⼒インピーダンスが0 • いくらでも電流を供給できる. • どのような周波数の信号でも同じように増幅する. + 入力端子は同じ電圧 • イマジナリショート(バーチャルショート,仮想短絡) • 反転端子と非反転端子はショートしている(同じ電圧)と考えて良い. 太字の2点を使いこなせればオペアンプの問題は大体解ける!!

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オペアンプを使った応⽤回路 • ⾮反転増幅回路 • 反転増幅回路 • ボルテージフォロア • 加算回路 • 減算回路

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⾮反転増幅回路

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⾮反転増幅回路 • オペアンプを⽤いた典型的な増幅回路 入力 出力 増幅器 • ⼊⼒は⾮反転⼊⼒に⼊る. • 出⼒端⼦から反転⼊⼒端⼦へ負帰還がある. 出力 Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">AAACZnichVHLSsNAFD2Nr1ofrYoouCmWiqsyLaLiqujGZR/2AbWUJE5raJqEJC3U4g8Ibu3ClYKI+Blu/AEX/QPFZQU3LrxJA6JFvcPMnDlzz50zM5KhKpbNWM8njIyOjU/4JwNT0zOzwdDcfN7Sm6bMc7Ku6mZREi2uKhrP2Yqt8qJhcrEhqbwg1fec/UKLm5aiawd22+DlhljTlKoiizZR2UylWglFWIy5ER4GcQ9E4EVKD93iEEfQIaOJBjg02IRViLColRAHg0FcGR3iTEKKu89xigBpm5TFKUMktk5jjVYlj9Vo7dS0XLVMp6jUTVKGEWVP7I712SO7Zy/s49daHbeG46VNszTQcqMSPFvOvv+ratBs4/hL9adnG1Vsu14V8m64jHMLeaBvnXT72Z1MtLPGrtkr+b9iPfZAN9Bab/JNmmcuEaAPiP987mGQT8Tim7FEeiOS3PW+wo8VrGKd3nsLSewjhRydW8M5LtD1PQuzwqKwNEgVfJ5mAd9CCH8CgnmKsg==</latexit> Rs <latexit sha1_base64="NiKYl+r+uCmxJsIofUKqa789ajc=">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</latexit> 入力 + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> Vf <latexit sha1_base64="RTtbx3Vc6h5PNN0pdMvKrjLaXxY=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

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⾮反転増幅回路の増幅度 • VoはRsとRfで分圧されるため, Rs Vf = Vo Rf + Rs <latexit sha1_base64="KrvOjJnBWj2a9vC/ia3zNx3VHqA=">AAACB3icbZBPS8MwGMZT/875r+pRkOAQBGG0Q9SLMPTicYrrBlspaZZuYWlSklQYZTcvfhUvHhTx6lfw5rcx3XrQzRcSfjzP+5K8T5gwqrTjfFsLi0vLK6ultfL6xubWtr2z6ymRSkyaWDAh2yFShFFOmppqRtqJJCgOGWmFw+vcbz0Qqajg93qUED9GfU4jipE2UmAfeEEEL2E3kghnd4EamyuCJzBHLxCBXXGqzqTgPLgFVEBRjcD+6vYETmPCNWZIqY7rJNrPkNQUMzIud1NFEoSHqE86BjmKifKzyR5jeGSUHoyENIdrOFF/T2QoVmoUh6YzRnqgZr1c/M/rpDq68DPKk1QTjqcPRSmDWsA8FNijkmDNRgYQltT8FeIBMpFoE13ZhODOrjwPXq3qnlVrt6eV+lURRwnsg0NwDFxwDurgBjRAE2DwCJ7BK3iznqwX6936mLYuWMXMHvhT1ucPQLSYTA==</latexit> • イマジナリショートを適用するとViとVfは等しいと考えられるので Rs Vi = Vo Rf + Rs <latexit sha1_base64="J/Oi6jGxzt9J6jssRkTiBUBom1I=">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</latexit> Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> Rs <latexit sha1_base64="NiKYl+r+uCmxJsIofUKqa789ajc=">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</latexit> - • よって,電圧増幅度Avfは + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> <latexit sha1_base64="1pdd1kM00UgPE9gXhq5MC/KEAw8=">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</latexit> AV f Vo Rf + R s = = Vi Rs Vf <latexit sha1_base64="RTtbx3Vc6h5PNN0pdMvKrjLaXxY=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

19.

問題解説 • 図の回路においてViに3Vの信号を⼊⼒するとVoは何Vになるか. (32ME) 10kΩ 10kΩ 1. 1 - 2. 2 3. 3 4. 6 5. 12 + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

20.

問題解説 • 図の回路においてViに3Vの信号を⼊⼒するとVoは何Vになるか. (32ME) R1 R2 10kΩ あえて増幅度の公式を使わず解きます. 10kΩ 1. 1 2. 2 3V 3. 3 Vi + 4. 6 5. 12 Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit> <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> 3V バーチャルショートを適⽤すると,オペアンプのそ れぞれの⼊⼒端⼦の電圧は等しいと⾒なせるので, R1に3Vの電圧が加わっている. また,⼊⼒インピーダンスは無限⼤なので,⾮反転 ⼊⼒端⼦への接続は無視できる.そう考えれば,Vo はR1とR2で分圧されている(抵抗が直列につながっ ている)と考えられる.よって,R1に加わる電圧を VR1とすると, VR1 = R1/(R1+R2)Vo なので,Vo=6Vとなる. バーチャルショートだ から等しい 別解:R1とR2は等しいので,R2には3Vの電圧が加わる .よって Vo=Vr1+Vr2=3+3=6Vである.

21.

問題 • 図の理想オペアンプ回路で,端⼦AB間に1kΩの抵抗を接続した.出⼒ 端⼦Aと端⼦Cの間の電位差は何Vか.(第34回ME2種) 1. 1 2. 5 3. 7 4. 10 5. 12

22.

問題 • 図の理想オペアンプ回路で,端⼦AB間に1kΩの抵抗を接続した.出⼒ 端⼦Aと端⼦Cの間の電位差は何Vか.(第34回ME2種) 1. 1 2. 5 3. 7 4. 10 5. 12 イマジナリショートから,BC間の電位差は5Vで ある. BC間に流れる電流は 5 𝐼!" = 𝐴 1𝑘 ⼊⼒端⼦はインピーダンス無限⼤なので電流は 流れ込まない.よって,電流のすべてがAB間に 流れる.よってAB間の電位差は 𝑉#! = 𝐼!" ×1𝑘 = 5𝑉 よってAC間の電位差は 𝑉#" = 5 + 5 = 10𝑉

23.

第35回ME2種 • 理想オペアンプの回路で,可変抵抗Rvが1kΩのとき,端⼦AB間を流れ る電流がIoであった.可変抵抗を2kΩに変化させたとき,端⼦AB間を 流れる電流IはIoの何倍か. 1. ¼ 2. ½ 3. 1 4. 2 5. 4

24.

第35回ME2種 • 理想オペアンプの回路で,可変抵抗Rvが1kΩのとき,端⼦AB間を流れ る電流がIoであった.可変抵抗を2kΩに変化させたとき,端⼦AB間を 流れる電流IはIoの何倍か.(第35回ME2種) 1. ¼ 2. ½ 3. 1 4. 2 1V 5. 4 バーチャルショートだ から等しい I ⼊⼒インピーダンスは無限⼤なので,反転 ⼊⼒端⼦には電流が流れ込まない. つまり,出⼒端⼦から流れ出す電流のすべ てが1kΩの抵抗に流れる.よって,AB間に 流れる電流Iと1kΩの抵抗に流れる電流は等 しい. バーチャルショートより,1kΩの抵抗に加 わる電圧はRvの値によらず1Vである.つま り,Rvが変化しても,1kΩの抵抗に流れる 電流は変化しない. よって,AB間に流れる電流IはRvによって変 化しないから,IはIoの1倍である.

25.

反転増幅回路

26.

反転増幅回路 • ⼊⼒は反転⼊⼒端⼦へ • ⾮反転⼊⼒端⼦はGNDに接続 Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> Rs <latexit sha1_base64="NiKYl+r+uCmxJsIofUKqa789ajc=">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</latexit> Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

27.

反転増幅回路の増幅度 • 𝑅& に加わる電圧𝑉'# はイマジナリショートより • 𝑉'# = 𝑉( • 𝑅& を流れる電流𝐼'# は • 𝐼'# = #$# '# = #" '# • ⼊⼒端⼦には電流は⼊っていかないため,それぞれの抵抗を流れる電 流𝐼'# と𝐼'% は等しい.よって Rf Rs #" • 𝐼'# = 𝐼'% = ' <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> <latexit sha1_base64="NiKYl+r+uCmxJsIofUKqa789ajc=">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</latexit> # <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> • よって抵抗𝑅( に加わる電圧𝑉'% は • 𝑉'% = #" ×𝑅( '# = Vi '% '# ×𝑉) IRs IRf + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

28.

反転増幅回路の増幅度 • 𝑅( に流れる電流は出⼒⽅向なので𝑉* はGND側が+極の電源だと考える ことができる.つまり,負となる. • また,出⼒電圧は𝑅( にかかる電圧と等しいので • 𝑉* = −𝑉'% = − '% '# ×𝑉) • よって,増幅度は • 𝐴+( = #! #" =− Rs '% '# Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> <latexit sha1_base64="NiKYl+r+uCmxJsIofUKqa789ajc=">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</latexit> Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

29.

問題解説 • 図の回路で電流計の指⽰値は何mAか.ただし,演算増幅器と電流計は 理想的に働くこととする.(第34回ME2種) I 1. 1 2kΩ 2. 2 3. 3 4. 6 5. 12 6V 1kΩ A +

30.

問題解説 • 図の回路で電流計の指⽰値は何mAか.ただし,演算増幅器と電流計は 理想的に働くこととする.(第34回ME2種) 6V 3mA 1. 1 R1 2kΩ 2. 2 3. 3 4. 6 5. 12 R2 I 1kΩ A - 6V + 0V バーチャルショートを適⽤すると,オペア ンプのそれぞれの⼊⼒端⼦の電圧は等しいと ⾒なせるので,反転⼊⼒端⼦に加わる電圧は 0Vである.つまり,R1に加わる電圧は6Vと なる.よって,R1に流れる電流は6/2k=3mA である. また,⼊⼒インピーダンスは無限⼤なので ,電流は⼊⼒端⼦に⼊らない.つまり,R1に 流れる電流のすべてがR2に流れる.よって, Iは3mAである.

31.

ボルテージフォロア

32.

ボルテージフォロア • 電圧を増幅しない. • 増幅度は1. • イマジナリショートを適用すると,VI=Voとなることから分かる. • ⼊⼒インピーダンスが⼤きく,出⼒インピーダンスが⼩さいため,バ ッファとして使⽤される. • オペアンプが電流を供給する. • ボルテージフォロアを追加すると出⼒インピーダンスが⼩さくなるので, インピーダンスを変換しているとも⾔える. 補足:出力インピーダンスが小さいとは,アンプの電 流供給力が高いことを意味します.オームの法則 (V=RI)を考えれば,電流を供給できないと電圧が上が らないことはすぐ分かります.電圧が上がらないのは アンプで電圧降下が起こっているからだと考える事が できます.電圧降下は出力に抵抗があるからだと考え られます.その抵抗のインピーダンスが出力インピー + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">AAACZnichVG7SgNBFD1ZXzFqEhVRsAmGiFWYBFGxCtpY5mEeEEPYXce4ZF/sbgIx+AOCrSmsFETEz7DxByzyB4plBBsLbzYLokG9w8ycOXPPnTMzkqkqtsNY1yeMjI6NT/gnA1PTM8FQeHauYBsNS+Z52VANqySJNlcVnecdxVF5ybS4qEkqL0r13f5+scktWzH0fadl8oom1nTlSJFFh6hcoWpUw1EWZ25EhkHCA1F4kTbCtzjAIQzIaEADhw6HsAoRNrUyEmAwiaugTZxFSHH3OU4RIG2DsjhliMTWaazRquyxOq37NW1XLdMpKnWLlBHE2BO7Yz32yO7ZC/v4tVbbrdH30qJZGmi5WQ2dLeXe/1VpNDs4/lL96dnBEbZcrwp5N12mfwt5oG+edHq57Wysvcqu2Sv5v2Jd9kA30Jtv8k2GZy8RoA9I/HzuYVBIxhMb8WRmPZra8b7Cj2WsYI3eexMp7CGNPJ1bwzku0PE9C0FhQVgcpAo+TzOPbyFEPgGcgYq/</latexit>

33.

演習 • 図の回路について誤っているのはどれか.ただし,Aは理想演算増幅 器である.(第40回ME2種) 1. 電圧増幅度は1倍である. 2. インピーダンス変換機として使⽤される. 3. ⼊⼒インピーダンスは無限⼤である. 4. 正帰還が⽤いられている. - 5. 電圧フォロアである. + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

34.

演習 • 図の回路について誤っているのはどれか.ただし,Aは理想演算増幅 器である.(第40回ME2種) 1. 電圧増幅度は1倍である. バーチャルショートを考えれば当然です. 出⼒インピーダンスの⾼い機器にボルテージフォロアをつ 2. インピーダンス変換機として使⽤される.なぎ,ボルテージフォロアに電流を供給させることで出⼒ インピーダンスを下げます. 3. ⼊⼒インピーダンスは無限⼤である. オペアンプの⼊⼒端⼦に⼊⼒が⼊っているから. 4. 正帰還が⽤いられている. 負帰還です. 5. 電圧フォロアである. 回路の名前そのままです. + Vi <latexit sha1_base64="0mcWRBZE1AGyK5jAucXWyerq7vA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

35.

加算回路

36.

加算回路 • 複数の⼊⼒の電圧を加算する回路 • 反転増幅回路に複数の⼊⼒がある回路になっている. I1 <latexit sha1_base64="FE/9udgjNCGJBXZu4YwlP7+JRsk=">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</latexit> V1 R1 <latexit 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sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> I2 <latexit sha1_base64="Io9nQB369vX0AuO8heWnhxjYaqI=">AAACZnichVFNSwJBGH7cvsxKrYiCLpIYnWSUqOgkdambH/kBJrK7jba47i67q2DSHwi65qFTQUT0M7r0Bzr4D4qOBl069LouREn1DjPzzDPv884zM5KhKpbNWNcjjIyOjU94J31T0zP+QHB2LmfpDVPmWVlXdbMgiRZXFY1nbcVWecEwuViXVJ6Xarv9/XyTm5aiawd2y+CluljVlIoiizZRmf1yvBwMsyhzIjQMYi4Iw42kHrzFIY6gQ0YDdXBosAmrEGFRKyIGBoO4EtrEmYQUZ5/jFD7SNiiLU4ZIbI3GKq2KLqvRul/TctQynaJSN0kZQoQ9sTvWY4/snr2wj19rtZ0afS8tmqWBlhvlwNlS5v1fVZ1mG8dfqj8926hgy/GqkHfDYfq3kAf65kmnl9lOR9qr7Jq9kv8r1mUPdAOt+SbfpHj6Ej76gNjP5x4GuXg0thGNp9bDiR33K7xYxgrW6L03kcAeksjSuVWc4wIdz7PgFxaExUGq4HE18/gWQugTCGeKdQ==</latexit> Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> V3 <latexit sha1_base64="4R+Cp4jRTZhZibXU7A1yK6kPpaI=">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</latexit> I3 + <latexit sha1_base64="sondPqGNGuoIcJ9jxdZCr+SqPjA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

37.

加算回路の増幅度 • イマジナリショートを考えると反転⼊⼒端⼦は0Vと⾒なせるから,⼊ ⼒の各抵抗に流れる電流は I1 <latexit sha1_base64="FE/9udgjNCGJBXZu4YwlP7+JRsk=">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</latexit> V1 R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">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</latexit> I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> I2 <latexit sha1_base64="Io9nQB369vX0AuO8heWnhxjYaqI=">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</latexit> Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> V3 <latexit sha1_base64="4R+Cp4jRTZhZibXU7A1yK6kPpaI=">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</latexit> I3 + <latexit sha1_base64="sondPqGNGuoIcJ9jxdZCr+SqPjA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

38.

加算回路の増幅度 • 理想オペアンプの⼊⼒には電流は⼊っていかないので,電流はすべて Rfに流れる(電流保存則). I = I1 + I2 + I3 <latexit sha1_base64="14+nDxMv+25i9rQVHqjRVrh9P+g=">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</latexit> I1 <latexit sha1_base64="FE/9udgjNCGJBXZu4YwlP7+JRsk=">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</latexit> • よって出⼒電圧Voは V1 R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">AAACZnichVHLSsNAFD2Nr1q1rYoouCmWiqsyKaLiqujGZR/2AbWUJI41NE1CkhZq8QcEt3bhSkFE/Aw3/oCL/oHisoIbF96mAdGi3mFmzpy5586ZGdnUVNthrOsTRkbHxif8k4Gp6ZlgKDw7l7eNhqXwnGJohlWUJZtrqs5zjupovGhaXKrLGi/Itd3+fqHJLVs19H2nZfJyXarq6pGqSA5R2UxFrISjLM7ciAwD0QNReJEywrc4wCEMKGigDg4dDmENEmxqJYhgMIkro02cRUh19zlOESBtg7I4ZUjE1mis0qrksTqt+zVtV63QKRp1i5QRxNgTu2M99sju2Qv7+LVW263R99KiWR5ouVkJnS1l3/9V1Wl2cPyl+tOzgyNsuV5V8m66TP8WykDfPOn0stuZWHuVXbNX8n/FuuyBbqA335SbNM9cIkAfIP587mGQT8TFjXgivR5N7nhf4ccyVrBG772JJPaQQo7OreIcF+j4noWgsCAsDlIFn6eZx7cQIp8YeYp9</latexit> I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> I2 <latexit sha1_base64="Io9nQB369vX0AuO8heWnhxjYaqI=">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</latexit> Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> V3 <latexit sha1_base64="4R+Cp4jRTZhZibXU7A1yK6kPpaI=">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</latexit> 重ね合わせの原理が成り⽴つので,それぞれの抵 抗のみの回路で計算した結果を⾜し合わせれば良 い. I3 + <latexit sha1_base64="sondPqGNGuoIcJ9jxdZCr+SqPjA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

39.

加算回路の増幅度 • 出⼒電圧は • となる.これは,それぞれの⼊⼒電圧がそれぞれの抵抗によって異な った倍率で増幅されたものが⾜し合わされることを意味する. • もし, とすると,出⼒電圧Voは I1 <latexit sha1_base64="FE/9udgjNCGJBXZu4YwlP7+JRsk=">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</latexit> V1 R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">AAACZnichVHLSsNAFD2Nr1q1rYoouCmWiqsyKaLiqujGZR/2AbWUJI41NE1CkhZq8QcEt3bhSkFE/Aw3/oCL/oHisoIbF96mAdGi3mFmzpy5586ZGdnUVNthrOsTRkbHxif8k4Gp6ZlgKDw7l7eNhqXwnGJohlWUJZtrqs5zjupovGhaXKrLGi/Itd3+fqHJLVs19H2nZfJyXarq6pGqSA5R2UxFrISjLM7ciAwD0QNReJEywrc4wCEMKGigDg4dDmENEmxqJYhgMIkro02cRUh19zlOESBtg7I4ZUjE1mis0qrksTqt+zVtV63QKRp1i5QRxNgTu2M99sju2Qv7+LVW263R99KiWR5ouVkJnS1l3/9V1Wl2cPyl+tOzgyNsuV5V8m66TP8WykDfPOn0stuZWHuVXbNX8n/FuuyBbqA335SbNM9cIkAfIP587mGQT8TFjXgivR5N7nhf4ccyVrBG772JJPaQQo7OreIcF+j4noWgsCAsDlIFn6eZx7cQIp8YeYp9</latexit> I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> I2 <latexit sha1_base64="Io9nQB369vX0AuO8heWnhxjYaqI=">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</latexit> Rf <latexit sha1_base64="dXI0nens/V/Jrq2+2b86swEezZg=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">AAACZnichVHLSsNAFD2Nr1q1rYoouCmWiqsyKaLiqujGZR/2AbWUJI41NE1CkhZq8QcEt3bhSkFE/Aw3/oCL/oHisoIbF96mAdGi3mFmzpy5586ZGdnUVNthrOsTRkbHxif8k4Gp6ZlgKDw7l7eNhqXwnGJohlWUJZtrqs5zjupovGhaXKrLGi/Itd3+fqHJLVs19H2nZfJyXarq6pGqSA5R2UwlUQlHWZy5ERkGogei8CJlhG9xgEMYUNBAHRw6HMIaJNjUShDBYBJXRps4i5Dq7nOcIkDaBmVxypCIrdFYpVXJY3Va92varlqhUzTqFikjiLEndsd67JHdsxf28Wuttluj76VFszzQcrMSOlvKvv+rqtPs4PhL9adnB0fYcr2q5N10mf4tlIG+edLpZbczsfYqu2av5P+KddkD3UBvvik3aZ65RIA+QPz53MMgn4iLG/FEej2a3PG+wo9lrGCN3nsTSewhhRydW8U5LtDxPQtBYUFYHKQKPk8zj28hRD4BGnmKfg==</latexit> V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">AAACZnichVG7SgNBFD1ZXzFqEhVRsAmGiFWYBFGxCtpY5mEeEEPYXce4ZF/sbgIx+AOCrSmsFETEz7DxByzyB4plBBsLbzYLokG9w8ycOXPPnTMzkqkqtsNY1yeMjI6NT/gnA1PTM8FQeHauYBsNS+Z52VANqySJNlcVnecdxVF5ybS4qEkqL0r13f5+scktWzH0fadl8oom1nTlSJFFh6hcoZqshqMsztyIDIOEB6LwIm2Eb3GAQxiQ0YAGDh0OYRUibGplJMBgEldBmziLkOLuc5wiQNoGZXHKEImt01ijVdljdVr3a9quWqZTVOoWKSOIsSd2x3rskd2zF/bxa622W6PvpUWzNNBysxo6W8q9/6vSaHZw/KX607ODI2y5XhXybrpM/xbyQN886fRy29lYe5Vds1fyf8W67IFuoDff5JsMz14iQB+Q+Pncw6CQjCc24snMejS1432FH8tYwRq99yZS2EMaeTq3hnNcoON7FoLCgrA4SBV8nmYe30KIfAIigYqC</latexit> R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> V3 <latexit sha1_base64="4R+Cp4jRTZhZibXU7A1yK6kPpaI=">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</latexit> I3 + <latexit sha1_base64="sondPqGNGuoIcJ9jxdZCr+SqPjA=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

40.

問題 • 図の回路の出⼒電圧Vo[V]はどれか.ただし,Aは理想演算増幅器とす る.(第42回ME2種) 1. -5.5 2. -5.0 3. 0 4. 5.0 5. 5.0

41.

問題 • 図の回路の出⼒電圧Vo[V]はどれか.ただし,Aは理想演算増幅器とす 1 𝐴 る.(第42回ME2種) 10𝑘 1. -5.5 2. -5.0 3. 0 4. 5.0 5. 5.5 ⼊⼒側の抵抗を⼀つづつ考える. 10kΩの抵抗のみがある場合を考える. 抵抗に流れる電流は,イマジナリショートから 1 𝐼$ = 𝐴 10𝑘 ⼊⼒端⼦はインピーダンスが無限⼤なので,これ が50kΩにも流れる.よって出⼒電圧は 𝑣%$ = −5𝑉 20kΩの抵抗のみがある場合を考える. 先程と同様に計算すると出⼒電圧は 0.2 𝑣%& = − ×50k = −0.5V 20𝑘 よって,出⼒電圧は 𝑣% = 𝑣%$ + 𝑣%& = −5.5𝑉 -5V 0.1 𝐴 10𝑘 -0.5V

42.

問題解説 • 図の回路の出⼒電圧Vo[V]はいくらか.(第37回ME2種) 20kΩ 1. -4 -1V 40kΩ 2. -1 3. 1 4. 2 80kΩ 1V 1V 80kΩ + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit> 5. 4

43.

問題解説 • 図の回路の出⼒電圧Vo[V]はいくらか.(第37回ME2種) 20kΩ 1. -4 -1V 40kΩ 2. -1 3. 1 4. 2 80kΩ 1V 1V 80kΩ + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit> 5. 4 加算回路は重ね合わせで考えることが できる. 20kΩの⼊⼒のみに考えると,出⼒は 4Vである. 40kΩの⼊⼒のみに考えると,出⼒は − 2Vである. 80kΩの⼊⼒のみに考えると,出⼒は − 1Vである. よって出⼒は 𝑉% = 4 − 2 − 1 = 1𝑉

44.

問題解説 • 図の回路の出⼒電圧Vo[V]はいくらか.(第37回ME2種) I1 20kΩ 1. -4 2. -1 3. 1 4. 2 I=I1+I2+I3 -1V I2 40kΩ I3 80kΩ 1V 1V 80kΩ + Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit> 5. 4 別解 バーチャルショートを適⽤すると,反転⼊ ⼒端⼦の電圧は⾮反転⼊⼒端⼦と同じなと⾒ なせるので0Vである.よって,抵抗に流れる 電流I1,I2,I3は I1=-1V/20kΩ= −0.05mA I2=1V/40kΩ=0.025mA I3=1V/80kΩ=0.0125mA となる.電流は⼊⼒端⼦に⼊らないので,す べて出⼒とつながる80kΩの抵抗へ流れる. よってIは, I=I1+I2+I3= −0.0125mA となる.反転⼊⼒は0Vなので,出⼒とつなが る80kΩの抵抗に加わる電圧が出⼒電圧Voと なる.また,電流は電圧の⾼い⽅から低い⽅ に流れるため,Voは正である.よって Vo=0.0125mA*80kΩ=1V

45.

減算回路

46.

減算回路 • 減算回路は2つの⼊⼒電圧の差に⽐例した電圧を出⼒する. I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">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</latexit> V1 <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> - R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> + V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> V20 <latexit sha1_base64="//Bzw0R7XjLqiFXFSM8DrMOJkb8=">AAACZ3ichVHLSsNAFD2N7/poVZCCG7X4WJXbIiquRDcu+7BVUClJHDU0TUIyLdTiD7hwq+BKQUT8DDf+gIt+grhUcOPCmzQgKuodZubMmXvunJnRHNPwJFEronR0dnX39PZF+wcGh2Lx4ZGSZ9dcXRR127TdLU31hGlYoigNaYotxxVqVTPFplZZ8/c368L1DNvakA1H7FbVA8vYN3RV+lRptpwpx5OUoiAmfoJ0CJIII2vHb7CDPdjQUUMVAhYkYxMqPG7bSIPgMLeLJnMuIyPYFzhGlLU1zhKcoTJb4fGAV9sha/Har+kFap1PMbm7rJzAND3SLb3QA93RE73/WqsZ1PC9NHjW2lrhlGMnicLbv6oqzxKHn6o/PUvsYynwarB3J2D8W+htff3o7KWwnJ9uztAVPbP/S2rRPd/Aqr/q1zmRv0CUPyD9/bl/glImlV5IZXLzyZXV8Ct6MY4pzPF7L2IF68iiyOce4hRnOI88KTFlTEm0U5VIqBnFl1AmPwCWiYqz</latexit> R4 <latexit sha1_base64="PzQOnZ40v2ecm62vLfPzYoIv3CQ=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

47.

減算回路の出⼒ • ⾮反転⼊⼒端⼦の電圧Vʼ2は,R4に加わる電圧なので <latexit sha1_base64="zpl7cFlvdKZGrpuWmKn8CNYQCzE=">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</latexit> V20 R4 = V2 R 3 + R4 • イマジナリーショートを考慮すると,非反転入力端子の電圧と反転入 I 力端子の電圧は等しい. <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> • したがって,R1に流れる電流Iは, <latexit sha1_base64="rH+Z6CsydzCCZrR/nVWdunWFaPA=">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</latexit> I= V20 V1 R1 R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">AAACZnichVHLSsNAFD2Nr1q1rYoouCmWiqsyKaLiqujGZR/2AbWUJI41NE1CkhZq8QcEt3bhSkFE/Aw3/oCL/oHisoIbF96mAdGi3mFmzpy5586ZGdnUVNthrOsTRkbHxif8k4Gp6ZlgKDw7l7eNhqXwnGJohlWUJZtrqs5zjupovGhaXKrLGi/Itd3+fqHJLVs19H2nZfJyXarq6pGqSA5R2UwlUQlHWZy5ERkGogei8CJlhG9xgEMYUNBAHRw6HMIaJNjUShDBYBJXRps4i5Dq7nOcIkDaBmVxypCIrdFYpVXJY3Va92varlqhUzTqFikjiLEndsd67JHdsxf28Wuttluj76VFszzQcrMSOlvKvv+rqtPs4PhL9adnB0fYcr2q5N10mf4tlIG+edLpZbczsfYqu2av5P+KddkD3UBvvik3aZ65RIA+QPz53MMgn4iLG/FEej2a3PG+wo9lrGCN3nsTSewhhRydW8U5LtDxPQtBYUFYHKQKPk8zj28hRD4BGnmKfg==</latexit> R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">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</latexit> V1 <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> - R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> + V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> V20 <latexit sha1_base64="//Bzw0R7XjLqiFXFSM8DrMOJkb8=">AAACZ3ichVHLSsNAFD2N7/poVZCCG7X4WJXbIiquRDcu+7BVUClJHDU0TUIyLdTiD7hwq+BKQUT8DDf+gIt+grhUcOPCmzQgKuodZubMmXvunJnRHNPwJFEronR0dnX39PZF+wcGh2Lx4ZGSZ9dcXRR127TdLU31hGlYoigNaYotxxVqVTPFplZZ8/c368L1DNvakA1H7FbVA8vYN3RV+lRptpwpx5OUoiAmfoJ0CJIII2vHb7CDPdjQUUMVAhYkYxMqPG7bSIPgMLeLJnMuIyPYFzhGlLU1zhKcoTJb4fGAV9sha/Har+kFap1PMbm7rJzAND3SLb3QA93RE73/WqsZ1PC9NHjW2lrhlGMnicLbv6oqzxKHn6o/PUvsYynwarB3J2D8W+htff3o7KWwnJ9uztAVPbP/S2rRPd/Aqr/q1zmRv0CUPyD9/bl/glImlV5IZXLzyZXV8Ct6MY4pzPF7L2IF68iiyOce4hRnOI88KTFlTEm0U5VIqBnFl1AmPwCWiYqz</latexit> R4 <latexit sha1_base64="PzQOnZ40v2ecm62vLfPzYoIv3CQ=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

48.

減算回路の出⼒ これらの計算はおまけ,読み飛ばして良い I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> • よって出⼒電圧Voは R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">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</latexit> Vo <latexit sha1_base64="81kXE4nPfWX0NSgnUjSEBcWbu+w=">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</latexit> V 1 = R 1 I + R2 I V1 <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> - R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> = (R1 + R2 ) V20 V1 R1 + V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> R1 + R 2 0 R1 Vo = (V2 V1 + ) R1 R1 + R 2 R1 + R 2 R4 R2 = ( V2 V1 ) R1 R 3 + R4 R1 + R2 <latexit sha1_base64="4Sss8UQkRhsntL4NwemWIg2OZug=">AAAC9HichVHLSsNQEJ3EV62vqhuhm2CtD4rlJhYVQSi6cVmrjYKVkMRbDU2TkKSFWvoDbly60I1KERH8CTf+gAs/QVyquHHhJI1v1Am598yZOTNz71UsXXNcQm4ZtqW1rb0j1Bnu6u7p7Yv0D4iOWbZVmlNN3bTXFdmhumbQnKu5Ol23bCqXFJ2uKcVFL75WobajmcaqW7XoZkneNrSCpsouUlJkX5RMbnSeyxdsWa1lJZ5LcFlJqHuwPi6OSQI3yYk+/Z5S/5Q3kc+Hf5W/sSnPn0p4AGt5Fd8iwuda2GZCisRIkvjG/QR8AGIQWMaMnEEetsAEFcpQAgoGuIh1kMHBbwN4IGAhtwk15GxEmh+nUIcwasuYRTFDRraI6zZ6GwFroO/VdHy1il10/G1UchAnN+ScPJBrckHuyMuvtWp+DW+WKu5KU0stqW9vaOX5X1UJdxd2PlR/zuxCAWb9WTWc3fIZ7xRqU1/ZPXhYmcvGa6PkhNzj/MfkllzhCYzKo9pYptlDCOMD8N+v+ycQhSQ/nRSWU7H0QvAUIYjCMIzjfc9AGpYgAzns+8REmREmzlbYI/aUbTRTWSbQDMIXYy9fAe+AtsY=</latexit> V20 <latexit sha1_base64="//Bzw0R7XjLqiFXFSM8DrMOJkb8=">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</latexit> R4 <latexit sha1_base64="PzQOnZ40v2ecm62vLfPzYoIv3CQ=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

49.

減算回路の出⼒ • また, <latexit sha1_base64="zh4rkwv1pUzNcPLfSbg1BjR8TCw=">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</latexit> これらの計算はおまけ,読み飛ばして良い とすると, R1 + R 2 R4 R2 ( V2 V1 ) R1 R3 + R4 R 1 + R2 R4 /R3 R2 /R1 = (1 + R2 /R1 )( V2 V1 ) 1 + R4 /R3 1 + R2 /R1 R2 /R1 R2 /R1 = (1 + R2 /R1 )( V2 V1 ) 1 + R2 /R1 1 + R2 /R1 R2 = (V2 V1 ) R1 Vo = • となり,v1とv2の差が求められる. I <latexit sha1_base64="hHesWnk/jX/rSH8+wlPSYTrXbCU=">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</latexit> R2 <latexit sha1_base64="/JKNrhreI3pIA66StGDK7GWCJoE=">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</latexit> R1 <latexit sha1_base64="Uv1aZX+6SbbobBDrSG78N7FPHkQ=">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</latexit> V1 <latexit sha1_base64="fF4U4ZWhw3WUSn6dPzDO0REzEek=">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</latexit> - R3 <latexit sha1_base64="J2nDiKOIxaF1nCbBwZBTTOrXMNA=">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</latexit> + V2 <latexit sha1_base64="A95NPp0CSpuO9mcyOG87PD4PoLE=">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</latexit> V20 <latexit sha1_base64="//Bzw0R7XjLqiFXFSM8DrMOJkb8=">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</latexit> R4 <latexit sha1_base64="PzQOnZ40v2ecm62vLfPzYoIv3CQ=">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</latexit> Vo <latexit sha1_base64="KKMMeSpBVdArWsob8SOFbOL0jU0=">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</latexit>

50.

問題解説 • 図の回路の⼊⼒端⼦aが開放状態であるときVaは何Vか.ただし,Aは 理想演算増幅器である.(第40回ME2種) a 1. 0 1kΩ 1kΩ 1kΩ - Va 2. 0.5 + 3. 1 4. 2 5. 5 1V 1kΩ A

51.

問題解説 • 図の回路の⼊⼒端⼦aが開放状態であるときVaは何Vか.ただし,Aは 理想演算増幅器である.(第40回ME2種) 1. 0 2. 0.5 1kΩ a Va 1kΩ 0.5V 1kΩ 3. 1 4. 2 5. 5 - A + 1V 1kΩ R VR = 0.5V バーチャルショートを適⽤すると,⾮反 転⼊⼒端⼦につながる抵抗Rに加わる電圧 VRと⾮反転⼊⼒端⼦の電圧は等しいと⾒ なせる.また,VRは1Vが2つの1kΩの抵抗 で分圧であるので,0.5Vである. Vaは,1kΩの抵抗とaとGND間の抵抗で 分圧すれば求まる.aとGND間の抵抗値は 開放なので無限⼤であるため,aとGND間 にすべての電圧が加わる.よって,Vaは 0.5Vである.

52.

問題 • 図のオペアンプ回路で,𝑅, はサーミスタである.抵抗𝑅! から𝑅- はすべ て10kΩである.𝑅, が10kΩのとき出⼒𝑉* はゼロであった.温度が上昇 し 𝑅, が9kΩに変化したとすると,出⼒電圧 𝑉* は何Vになるか.ただし, オペアンプは理想的とする.(第34回ME2種) 1. 10 2. 4.5 3. −0.5 4. −4.5 5. −10

53.

問題 • 図のオペアンプ回路で,𝑅, はサーミスタである.抵抗𝑅$ から𝑅- はすべて10kΩである.𝑅, が10kΩの とき出⼒ 𝑉% はゼロであった.温度が上昇し 𝑅, が9kΩに変化したとすると,出⼒電圧 𝑉% は何Vになるか. ただし,オペアンプは理想的とする.(第34回ME2種) 1. 10 2. 4.5 3. −0.5 4. −4.5 5. −10 𝑅- にかかる電圧は9/2=4.5Vである. イマジナリショートから抵抗𝑅, にかかる電 圧は,9 − 4.5 = 4.5である. よって抵抗𝑅, を流れる電流は 4.5 𝐼.! = A 9k である.この電流が抵抗𝑅$ に流れるので, 抵抗𝑅$ にかかる電圧 𝑉." は 4.5 𝑉." = ×10𝑘 = 5𝑉 9k である.よって出⼒電圧は 𝑉% = 9 − 4.5 − 𝑉." = −0.5V 出⼒電圧=⼊⼒電圧ーRtの電圧降下ーR1の電圧降下

54.

同相除去⽐

55.

同相除去⽐ • 差動増幅回路の各⼊⼒端⼦に⼊⼒v1,v2を与えたとき出⼒がvoだとする. 𝑣9 , 𝑣: , 𝑣; の関係は次のように書ける. • 𝑣9 = 𝐴< 𝑣: − 𝑣; + • Adは差動増幅度 • Acは同相増幅度 : 𝐴 (𝑣 ; = : 𝑣" + 𝑣; ) 𝑣! • 差動増幅度と同相増幅度の⽐を同相除去⽐CMRRという. • CMRR = &/ &0 • 同相除去⽐をdBで表すと • 𝐶𝑀𝑅𝑅 = 20 log'( &/ &0 • 同相除去⽐が⼤きいほど良い差動増幅回路である. • 理想オペアンプの場合 • 差動利得は無限⼤ • 同相除去⽐も無限⼤ + 𝑣#

56.

問題 • 同相利得が0.10倍,差動利得が200倍の差動増幅器がある。この増幅 器のCMRR(同相弁別⽐)は何dBか。ただし,log102=0.30とする。( 第41回ME2種) 1. 6 2. 40 3. 46 4. 60 5. 66

57.

問題 • 同相利得が0.10倍,差動利得が200倍の差動増幅器がある。この増幅 器のCMRR(同相弁別⽐)は何dBか。ただし,log102=0.30とする。( 第41回ME2種) 1. 6 2. 40 3. 46 4. 60 5. 66 定義通りに計算する 𝐶𝑀𝑅𝑅 = 20 log$1 𝐴2 /𝐴3 = 20 log$1 200 = 20 log$1 2×1000 = 20 3 + 0.3 = 66 0.1

58.

問題 • 同相除去⽐100dBの差動増幅器で,差動利得は60dBであった.同相利 得はいくらか.(第42回ME2種) 1. 60dB 2. 40dB 3. 20dB 4. -20dB 5. -40dB

59.

問題 • 同相除去⽐100dBの差動増幅器で,差動利得は60dBであった.同相利 得はいくらか.(第42回ME2種) 1. 60dB 2. 40dB 3. 20dB 4. -20dB 5. -40dB 同相除去⽐の定義から 𝐴* 𝐶𝑀𝑅𝑅 = 20 log'( = 20 log'( 𝐴* − 20 log'( 𝐴+ 𝐴+ = 60 − 20 log'( 𝐴+ = 100 よって 20 log'( 𝐴+ = − 100 − 60 = −40

60.

問題 • CMRR(同相除去⽐)が80dBの差動増幅器がある.差動増幅器の⼊⼒ 端⼦間に1mVを⼊⼒すると1Vが出⼒された.差動増幅器の2つの⼊⼒ 端⼦を短絡し,アースとの間に1Vを⼊⼒すると出⼒電圧は何Vになる か.(第37回ME2種) 1. 0.01 2. 0.1 3. 1 4. 10 5. 100

61.

問題 • CMRR(同相除去⽐)が80dBの差動増幅器がある.差動増幅器の⼊⼒ 端⼦間に1mVを⼊⼒すると1Vが出⼒された.差動増幅器の2つの⼊⼒ 端⼦を短絡し,アースとの間に1Vを⼊⼒すると出⼒電圧は何Vになる か.(第37回ME2種) 1. 0.01 2. 0.1 3. 1 4. 10 5. 100 1mV - 1V + 1V + 差動増幅 差動増幅度はAd=1/0.001=1000 同相除去⽐は 𝐴% CMRR = 20 log!$ = 20 log!$ 1000/𝐴& = 80 𝐴& 1000/𝐴& = 10' !$$$ 同相増幅度は 𝐴& = !$$$$ = 0.1 よって出⼒電圧は0.1V 同相増幅 ?

62.

問題 • 増幅率40dB,CMRR100dBの増幅器に,1.2Vの雑⾳(同相信号)が⼊ ⼒された.出⼒に現れる雑⾳の⼤きさはどれか.(第36回ME2種) 1. 48V 2. 30mV 3. 12mV 4. 1.2mV 5. 12μV

63.

第36回ME2種 • 増幅率40dB,CMRR100dBの増幅器に,1.2Vの雑⾳(同相信号)が⼊ ⼒された.出⼒に現れる雑⾳の⼤きさはどれか.(第36回ME2種) 1. 48V 2. 30mV 3. 12mV 4. 1.2mV 5. 12μV 増幅利得が40dBなので差動増幅度は 20 log'( 𝐴* = 40 よってAd=100である. CMRRが100dBなので同相増幅度は 100 20 log'( = 100 𝐴+ 100 = 10: 𝐴+ 10; 𝐴+ = : = 10<= 10 よって出⼒に現れる雑⾳は 1.2×10<=V = 1.2mV

64.

⼊⼒インピーダンス

65.

⼊⼒インピーダンスについて • 増幅器の⼊⼒抵抗(⼊⼒インピーダンス)は⼤きいほどよい. • 増幅器へ⼊⼒する機器の負荷が⼩さい. • 例えば⼊⼒インピーダンス1kΩの増幅回路に1Vの電圧を加えるために必要な電 流は1mAである.よって電⼒は1mW必要である.しかし,⼊⼒インピーダンス が1Ωの場合1Vの電圧を加えるためには電流は1Aである.よって電⼒は1W必要 となる. • つまり,増幅器の⼊⼒インピーダンスは⾼ければ⾼いほど必要な電⼒が下がるた め,それに接続する機器の負担は⼩さくなる. • 増幅器へ⼊⼒する機器の影響が少ない. • 図のように機器の出⼒に内部抵抗がある場合,機器の出⼒Vがその内部抵抗と⼊ ⼒インピーダンスで分圧される. • つまり,⼊⼒インピーダンスが⼤きければ⼤きいほど増幅器に加わる電圧が⼤き くなる.(内部抵抗の影響が少なくなる.) 抵抗 V 機器 +

66.

第35回ME2種 • ⼊⼒抵抗1MΩ,電圧増幅率110倍の直流増幅器に,図のように直流信 号を⼊⼒した.信号源の内部抵抗を100kΩ,直流電圧を10mVとする と,増幅器の出⼒[V]はいくらか. 1. 0.1 2. 0.5 3. 1.0 4. 1.1 5. 10.0

67.

第35回ME2種 • ⼊⼒抵抗1MΩ,電圧増幅率110倍の直流増幅器に,図のように直流信 号を⼊⼒した.信号源の内部抵抗を100kΩ,直流電圧を10mVとする と,増幅器の出⼒[V]はいくらか. 1. 0.1 2. 0.5 3. 1.0 4. 1.1 5. 10.0 入力電圧は内部抵抗と入力抵抗で分圧される. 入力抵抗に加わる電圧は, !"""# 10× = 10/1.1mV !!""# これが110倍に増幅されるので,出力電圧は 10 ×110 = 1000mV = 1V 1.1

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第35回ME2種 • 脳波計の増幅器の⼊⼒インピーダンスを⾼くする理由はなにか. 1. 検出信号の起電⼒が⼩さいため. 2. 直流を増幅するため. 3. 電極の接触インピーダンスが⾼いため. 4. 筋電図の混⼊を防ぐため. 5. 電極接触電圧による飽和を防ぐため.

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第35回ME2種 • 脳波計の増幅器の⼊⼒インピーダンスを⾼くする理由はなにか. 1. 検出信号の起電⼒が⼩さいため. 起電⼒が⼩さいから増幅器を使い⼤きくする. 2. 直流を増幅するため. 直流はカップリングコンデンサを使い除去する. 3. 電極の接触インピーダンスが⾼いため. 脳波は,接触インピーダンスと⼊⼒インピーダンスで分圧される.増幅器に なるべく⼤きな電圧を加えるために,⼊⼒インピーダンスを⼤きくしたほう が良い. 4. 筋電図の混⼊を防ぐため. 関係ない. 5. 電極接触電圧による飽和を防ぐため. 接触インピーダンス 入力インピーダンス 脳波