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對于(yu)正弦信號(hao)，流過一個元器件的(de)(de)電(dian)流和其兩端的(de)(de)電(dian)壓(ya)，它們的(de)(de)相位不一定是相同(tong)的(de)(de)。

 

這種(zhong)相位(wei)差(cha)是如何產生的呢？這種(zhong)知識非(fei)常重要(yao)，因為(wei)不僅放大器、自激振(zhen)蕩器的反饋信(xin)號要(yao)考慮(lv)相位(wei)，而且(qie)在構(gou)造一個電路(lu)時也需要(yao)充分了解、利用或避免這種(zhong)相位(wei)差(cha)。下面(mian)探討這個問題。

 

首先，要(yao)了(le)解(jie)一下一些元件是如(ru)何構(gou)建出(chu)來的(de)；其次，要(yao)了(le)解(jie)電(dian)路元器件的(de)基本工作原(yuan)理；第三(san)，據此找到(dao)理解(jie)相(xiang)位差(cha)產生(sheng)的(de)原(yuan)因；第四，利用元件的(de)相(xiang)位差(cha)特性構(gou)造一些基本電(dian)路。

 

一、電阻(zu)、電感、電容的誕生過程

 

科(ke)學家經(jing)過長期的(de)觀察、試(shi)驗(yan)，弄清楚(chu)了一些(xie)道理，也經(jing)常(chang)出現了一些(xie)預料之外的(de)偶然發(fa)現，如倫琴發(fa)現X射線、居(ju)里夫(fu)人(ren)發(fa)現鐳(lei)的(de)輻射現象，這些(xie)偶然的(de)發(fa)現居(ju)然成(cheng)了偉大的(de)科(ke)學成(cheng)就。電子(zi)學領域也是(shi)如此。

 

科(ke)學家(jia)讓電(dian)(dian)流(liu)(liu)流(liu)(liu)過導(dao)線的時候，偶(ou)然發(fa)現(xian)(xian)(xian)了導(dao)線發(fa)熱、電(dian)(dian)磁感應現(xian)(xian)(xian)象(xiang)，進(jin)而發(fa)明了電(dian)(dian)阻、電(dian)(dian)感。科(ke)學家(jia)還從(cong)摩擦起(qi)電(dian)(dian)現(xian)(xian)(xian)象(xiang)得到靈感，發(fa)明了電(dian)(dian)容。發(fa)現(xian)(xian)(xian)整流(liu)(liu)現(xian)(xian)(xian)象(xiang)而創造出二極管也是偶(ou)然。

 

二、元(yuan)器件(jian)的基(ji)本工作(zuo)原理

 

電(dian)阻(zu)——電(dian)能→熱能

 

電(dian)感——電(dian)能→磁場(chang)能，&磁場(chang)能→電(dian)能

 

電(dian)容——電(dian)勢能→電(dian)場能，&電(dian)場能→電(dian)流

 

由此可見，電(dian)阻(zu)、電(dian)感、電(dian)容(rong)(rong)就(jiu)是能(neng)源轉(zhuan)換(huan)的(de)元(yuan)件。電(dian)阻(zu)、電(dian)感實現不同種類能(neng)量(liang)間(jian)的(de)轉(zhuan)換(huan)，電(dian)容(rong)(rong)則實現電(dian)勢(shi)能(neng)與電(dian)場能(neng)的(de)轉(zhuan)換(huan)。

 

1、電阻

 

電阻的(de)原(yuan)理是：電勢能→電流→熱(re)能。

 

電(dian)(dian)源正(zheng)負兩端貯藏有(you)電(dian)(dian)勢(shi)(shi)能（正(zheng)負電(dian)(dian)荷），當電(dian)(dian)勢(shi)(shi)加在(zai)電(dian)(dian)阻(zu)兩端，電(dian)(dian)荷在(zai)電(dian)(dian)勢(shi)(shi)差作用下流(liu)動(dong)(dong)(dong)——形成(cheng)了電(dian)(dian)流(liu)，其流(liu)動(dong)(dong)(dong)速度遠比無電(dian)(dian)勢(shi)(shi)差時的亂序自由運(yun)動(dong)(dong)(dong)快，在(zai)電(dian)(dian)阻(zu)或(huo)導(dao)體內碰撞(zhuang)產(chan)生的熱(re)量也就更多(duo)。

 

正電(dian)荷從電(dian)勢高的(de)一端進入電(dian)阻(zu)，負電(dian)荷從電(dian)勢低的(de)一端進入電(dian)阻(zu)，二(er)者在電(dian)阻(zu)內部進行中(zhong)和作用。

 

中和作(zuo)用使得正(zheng)電荷數量(liang)在電阻(zu)(zu)內部呈現(xian)從(cong)高(gao)電勢(shi)(shi)端(duan)到低電勢(shi)(shi)端(duan)的(de)(de)梯度分布，負(fu)電荷數量(liang)在電阻(zu)(zu)內部呈現(xian)從(cong)低電勢(shi)(shi)端(duan)到高(gao)電勢(shi)(shi)端(duan)的(de)(de)梯度分布，從(cong)而在電阻(zu)(zu)兩端(duan)產生了電勢(shi)(shi)差，這就(jiu)是電阻(zu)(zu)的(de)(de)電壓(ya)降(jiang)。

 

同(tong)樣(yang)電流下(xia)，電阻對(dui)中和作用的阻力越大，其兩端電壓降也越大。

 

因此，用R=V/I來衡量線性電阻(zu)(zu)（電壓降與通(tong)過的電流成(cheng)正比）的阻(zu)(zu)力大小。

 

對交流(liu)信號則表達為R=v(t)/i(t)。

 

注意：也有非線性電阻的概念，其(qi)非線性有電壓影響型、電流影響型等。

 

2、電感

 

電感的原理：電感——電勢能→電流(liu)→磁場(chang)(chang)能，&磁場(chang)(chang)能→電勢能（若有負載，則→電流(liu)）。

 

當電(dian)(dian)(dian)源(yuan)電(dian)(dian)(dian)勢加在(zai)電(dian)(dian)(dian)感線圈兩(liang)端，電(dian)(dian)(dian)荷在(zai)電(dian)(dian)(dian)勢差作(zuo)用下流(liu)動(dong)——形(xing)成(cheng)了電(dian)(dian)(dian)流(liu)，電(dian)(dian)(dian)流(liu)轉(zhuan)變磁(ci)場，這(zhe)稱為(wei)“充磁(ci)”過程。

 

若(ruo)被(bei)充磁(ci)(ci)電(dian)(dian)感線圈(quan)兩端的電(dian)(dian)源電(dian)(dian)勢差撤銷，且電(dian)(dian)感線圈(quan)外接(jie)有負載，則磁(ci)(ci)場能(neng)在衰減的過程(cheng)中轉(zhuan)換為(wei)電(dian)(dian)能(neng)（如負載為(wei)電(dian)(dian)容，則為(wei)電(dian)(dian)場能(neng)；若(ruo)負載為(wei)電(dian)(dian)阻，則為(wei)電(dian)(dian)流），這稱為(wei)“去磁(ci)(ci)”過程(cheng)。

 

衡量電感線圈(quan)充磁(ci)多少的單位(wei)是(shi)磁(ci)鏈——Ψ。電流越大，電感線圈(quan)被沖磁(ci)鏈就越多，即磁(ci)鏈與電流成(cheng)正比，即Ψ=L*I。對一個指定(ding)電感線圈(quan)，L是(shi)常量。

 

因此，用L=Ψ/I表(biao)達電(dian)感(gan)線圈(quan)的電(dian)磁轉換(huan)能力，稱L為電(dian)感(gan)量(liang)。電(dian)感(gan)量(liang)的微分表(biao)達式為：L=dΨ(t)/di(t)。

 

根(gen)據電(dian)磁(ci)感應(ying)原理，磁(ci)鏈(lian)變化產(chan)生感應(ying)電(dian)壓(ya)，磁(ci)鏈(lian)變化越大則感應(ying)電(dian)壓(ya)越高，即v(t)=d dΨ(t)/dt。

 

綜合上面兩公式得到：v(t)=L*di(t)/dt，即電感(gan)的(de)(de)感(gan)應電壓(ya)與電流(liu)的(de)(de)變化率(lv)（對時間的(de)(de)導數）成正(zheng)比(bi)，電流(liu)變化越(yue)快則(ze)感(gan)應電壓(ya)越(yue)高。

 

3、電容

 

電(dian)(dian)容的原理：電(dian)(dian)勢能→電(dian)(dian)流→電(dian)(dian)場(chang)能，電(dian)(dian)場(chang)能→電(dian)(dian)流。

 

當電(dian)(dian)(dian)(dian)(dian)(dian)源電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)加在(zai)電(dian)(dian)(dian)(dian)(dian)(dian)容(rong)的(de)兩(liang)個(ge)(ge)金屬極(ji)(ji)板上，正負電(dian)(dian)(dian)(dian)(dian)(dian)荷(he)(he)在(zai)電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)差作用(yong)下(xia)分別向電(dian)(dian)(dian)(dian)(dian)(dian)容(rong)兩(liang)個(ge)(ge)極(ji)(ji)板聚集而形成電(dian)(dian)(dian)(dian)(dian)(dian)場，這稱為“充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)”過(guo)程(cheng)。若被充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)電(dian)(dian)(dian)(dian)(dian)(dian)容(rong)兩(liang)端(duan)的(de)電(dian)(dian)(dian)(dian)(dian)(dian)源電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)差撤銷，且電(dian)(dian)(dian)(dian)(dian)(dian)容(rong)外接有負載，則電(dian)(dian)(dian)(dian)(dian)(dian)容(rong)兩(liang)端(duan)的(de)電(dian)(dian)(dian)(dian)(dian)(dian)荷(he)(he)在(zai)其電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)差下(xia)向外流(liu)走，這稱為“放電(dian)(dian)(dian)(dian)(dian)(dian)”過(guo)程(cheng)。

 

電(dian)(dian)荷(he)在向電(dian)(dian)容(rong)(rong)聚集和從(cong)電(dian)(dian)容(rong)(rong)兩(liang)個極板向外流走(zou)的過程(cheng)中(zhong)，電(dian)(dian)荷(he)的流動就形成了(le)電(dian)(dian)流。

 

要特別(bie)注意，電(dian)(dian)(dian)容(rong)上的(de)(de)電(dian)(dian)(dian)流(liu)并不是(shi)電(dian)(dian)(dian)荷(he)真的(de)(de)流(liu)過(guo)(guo)電(dian)(dian)(dian)容(rong)兩(liang)個極(ji)板(ban)間的(de)(de)絕緣(yuan)介(jie)質，而(er)只是(shi)充電(dian)(dian)(dian)過(guo)(guo)程中(zhong)電(dian)(dian)(dian)荷(he)從外(wai)(wai)(wai)部(bu)向(xiang)電(dian)(dian)(dian)容(rong)兩(liang)個極(ji)板(ban)聚(ju)集形成的(de)(de)流(liu)動(dong)，以及放電(dian)(dian)(dian)過(guo)(guo)程中(zhong)電(dian)(dian)(dian)荷(he)從電(dian)(dian)(dian)容(rong)兩(liang)個極(ji)板(ban)向(xiang)外(wai)(wai)(wai)流(liu)走而(er)形成的(de)(de)流(liu)動(dong)。也(ye)就(jiu)是(shi)說(shuo)，電(dian)(dian)(dian)容(rong)的(de)(de)電(dian)(dian)(dian)流(liu)其實是(shi)外(wai)(wai)(wai)部(bu)電(dian)(dian)(dian)流(liu)，而(er)非(fei)內部(bu)電(dian)(dian)(dian)流(liu)，這(zhe)與電(dian)(dian)(dian)阻、電(dian)(dian)(dian)感(gan)都不一樣。

 

衡(heng)量電(dian)(dian)(dian)容充電(dian)(dian)(dian)多(duo)少的單位是電(dian)(dian)(dian)荷數(shu)——Q。電(dian)(dian)(dian)容極板(ban)間電(dian)(dian)(dian)勢差(cha)越大，說明(ming)電(dian)(dian)(dian)容極板(ban)被沖電(dian)(dian)(dian)荷越多(duo)，即(ji)電(dian)(dian)(dian)荷數(shu)與(yu)電(dian)(dian)(dian)勢差(cha)（電(dian)(dian)(dian)壓）成(cheng)正比，即(ji)Q=C*V。對指定電(dian)(dian)(dian)容，C是常量。

 

因此，用C=Q/V表達電(dian)容(rong)極(ji)板貯(zhu)存(cun)電(dian)荷的能力，稱C為電(dian)容(rong)量。

 

電容量的微分表達式為：C=dQ(t)/dv(t)。

 

因(yin)為電(dian)(dian)流(liu)等于單(dan)位時(shi)(shi)間內電(dian)(dian)荷數(shu)的變化(hua)量，即(ji)i(t)=dQ(t)/dt，綜合(he)上面(mian)兩個公(gong)式得到(dao)：i(t)=C*dv(t)/dt，即(ji)電(dian)(dian)容(rong)電(dian)(dian)流(liu)與其上電(dian)(dian)壓的變化(hua)率（對時(shi)(shi)間的導(dao)數(shu)）成正比，電(dian)(dian)壓變化(hua)越快(kuai)則電(dian)(dian)流(liu)越大。

 

4、小結：v(t)=L*di(t)/dt

 

表明電(dian)(dian)流變化形(xing)成了(le)電(dian)(dian)感(gan)的感(gan)應(ying)(ying)電(dian)(dian)壓（電(dian)(dian)流不變則沒有(you)感(gan)應(ying)(ying)電(dian)(dian)壓形(xing)成）。

i(t)=C*dv(t)/dt表明(ming)電(dian)(dian)壓變(bian)化形(xing)成了電(dian)(dian)容(rong)的(de)外部(bu)電(dian)(dian)流（實際(ji)是電(dian)(dian)荷量變(bian)化。電(dian)(dian)壓不變(bian)則沒有電(dian)(dian)容(rong)的(de)外部(bu)電(dian)(dian)流形(xing)成）。

 

三、元件對信號相(xiang)位的改變

 

首先(xian)要提(ti)醒，相位的概念是針對正(zheng)弦(xian)信(xin)號而言的，直流信(xin)號、非周期變化(hua)信(xin)號等都沒有相位的概念。

 

1、電阻上的電壓電流同相位

 

因為電(dian)阻(zu)上(shang)電(dian)壓v(t)=R*i(t)，若i(t)=sin(ωt+θ)，則(ze)v(t)=R* sin(ωt+θ)。所以(yi)，電(dian)阻(zu)上(shang)電(dian)壓與電(dian)流(liu)同相位。

 

2、電感上的電流落后電壓90°相位

 

因為電(dian)感(gan)(gan)(gan)上感(gan)(gan)(gan)應(ying)電(dian)壓(ya)v(t)=L*di(t)/dt，若i(t)=sin(ωt+θ)，則v(t)=L*cos(ωt+θ)。所以，電(dian)感(gan)(gan)(gan)上電(dian)流落(luo)后感(gan)(gan)(gan)應(ying)電(dian)壓(ya)90°相位，或(huo)者說感(gan)(gan)(gan)應(ying)電(dian)壓(ya)超前電(dian)流90°相位。

 

直(zhi)觀理解：設想一個電感與電阻串聯(lian)充(chong)磁(ci)。從充(chong)磁(ci)過程看，充(chong)磁(ci)電流的變化引起磁(ci)鏈的變化，而磁(ci)鏈的變化又產生(sheng)感應電動(dong)勢和感應電流。

 

根(gen)據楞次定律，感(gan)應(ying)電(dian)流方向與充(chong)磁(ci)電(dian)流相(xiang)反(fan)，延緩了(le)充(chong)磁(ci)電(dian)流的變化，使得充(chong)磁(ci)電(dian)流相(xiang)位(wei)落(luo)后于感(gan)應(ying)電(dian)壓。

 

3、電容上的電流超前電壓90°相位

 

因為電(dian)容(rong)上電(dian)流i(t)=C*dv(t)/dt，若v(t)=sin(ωt+θ)，則i(t)=L*cos(ωt+θ)。

 

所以，電容上電流超前電壓90°相(xiang)位，或者說電壓落后電流90°相(xiang)位。

 

直觀理解：設想一個電(dian)(dian)(dian)容(rong)與電(dian)(dian)(dian)阻串聯充(chong)電(dian)(dian)(dian)。從充(chong)電(dian)(dian)(dian)過程看，總是(shi)先(xian)有流動電(dian)(dian)(dian)荷（即電(dian)(dian)(dian)流）的(de)積累(lei)才(cai)有電(dian)(dian)(dian)容(rong)上(shang)的(de)電(dian)(dian)(dian)壓(ya)變化，即電(dian)(dian)(dian)流總是(shi)超前于(yu)電(dian)(dian)(dian)壓(ya)，或者說(shuo)電(dian)(dian)(dian)壓(ya)總是(shi)落后(hou)于(yu)電(dian)(dian)(dian)流。

 

下面的積分(fen)方程(cheng)能體現這種直(zhi)觀(guan)性：

 

v(t)=(1/C)*∫i(t)*dt=(1/C)*∫dQ(t)，即(ji)電(dian)荷變(bian)化的(de)積(ji)累形成了電(dian)壓，故(gu)dQ(t)相(xiang)位(wei)超前(qian)v(t)；而電(dian)荷積(ji)累的(de)過程(cheng)(cheng)就(jiu)是電(dian)流同步變(bian)化的(de)過程(cheng)(cheng)，即(ji)i(t)與dQ(t)同相(xiang)。因此i(t)相(xiang)位(wei)超前(qian)于(yu)v(t)。

 

四、元件相位差的應用

 

RC文(wen)氏橋、LC諧(xie)振過程(cheng)的(de)理解(jie)：無論RC文(wen)氏橋，還是(shi)LC的(de)串聯諧(xie)振、并聯諧(xie)振，都是(shi)由電容或(huo)/和電感容元件的(de)電壓、電流相(xiang)位(wei)差引起的(de)，就像機械共振的(de)節(jie)拍一樣。

當兩個(ge)頻(pin)率相同(tong)、相位(wei)相位(wei)的正弦波(bo)疊加(jia)時，疊加(jia)波(bo)的幅度(du)達(da)到(dao)最大值，這就是(shi)共振現(xian)象，在電(dian)路里稱為諧振。

 

兩(liang)個頻(pin)率相(xiang)(xiang)同、相(xiang)(xiang)位相(xiang)(xiang)反的(de)正弦波疊(die)加，疊(die)加波的(de)幅度會(hui)降到最低，甚至為零。這就是(shi)減(jian)小或吸收(shou)振動的(de)原理，如(ru)降噪設(she)備。

 

當一(yi)個(ge)(ge)系(xi)統中有多個(ge)(ge)頻(pin)率(lv)信(xin)號(hao)混合時，如果有兩個(ge)(ge)同頻(pin)信(xin)號(hao)產生了(le)共振(zhen)(zhen)，那么這(zhe)(zhe)個(ge)(ge)系(xi)統中其(qi)它振(zhen)(zhen)動頻(pin)率(lv)的(de)能量就(jiu)被這(zhe)(zhe)兩個(ge)(ge)同頻(pin)、同相的(de)信(xin)號(hao)所(suo)吸收，從而起到了(le)對其(qi)它頻(pin)率(lv)的(de)過濾(lv)作用。這(zhe)(zhe)就(jiu)是(shi)電(dian)路中諧振(zhen)(zhen)過濾(lv)的(de)原理。

 

諧振需要同(tong)時滿足頻(pin)率相同(tong)和相位(wei)相同(tong)兩(liang)個條件。電路如何通過幅度-頻(pin)率特(te)性選擇頻(pin)率的方法以前在RC文氏橋中(zhong)講過，LC串并聯的思路與RC相同(tong)，這(zhe)里不再(zai)贅述。

 

下(xia)面我(wo)們來看看電路諧振中相位(wei)補償(chang)的粗略估計(ji)（更精確的相位(wei)偏移則要計(ji)算）

 

1、RC文氏橋的諧振（圖1）

 

若(ruo)沒有C2，正(zheng)弦信號Uo的電(dian)流(liu)(liu)由(you)C1→R1→R2，通(tong)過R2上壓(ya)降形(xing)成Uf輸(shu)(shu)出電(dian)壓(ya)。由(you)于(yu)支路(lu)電(dian)流(liu)(liu)被電(dian)容C1移(yi)相(xiang)超(chao)前(qian)Uo 90°，這(zhe)超(chao)前(qian)相(xiang)位的電(dian)流(liu)(liu)流(liu)(liu)過R2（電(dian)阻不產生相(xiang)移(yi)！），使得輸(shu)(shu)出電(dian)壓(ya)Uf電(dian)壓(ya)超(chao)前(qian)于(yu)Uo 90°。

 

在(zai)R2上(shang)并聯(lian)C2，C2從(cong)R2取得(de)電(dian)(dian)壓(ya)(ya)，由于電(dian)(dian)容對電(dian)(dian)壓(ya)(ya)的滯(zhi)后作用，使(shi)得(de)R2上(shang)電(dian)(dian)壓(ya)(ya)也被(bei)強制滯(zhi)后。（但不(bu)一定有(you)(you)90°，因為還有(you)(you)C1→R1→C2電(dian)(dian)流對C2上(shang)電(dian)(dian)壓(ya)(ya)即(ji)Uf的影響(xiang)，但在(zai)RC特征頻率(lv)上(shang)，并聯(lian)C2后Uf輸出相位與(yu)Uo相同。）小(xiao)結：并聯(lian)電(dian)(dian)容使(shi)得(de)電(dian)(dian)壓(ya)(ya)信號相位滯(zhi)后，稱(cheng)為電(dian)(dian)壓(ya)(ya)相位的并聯(lian)補償。

 

2、LC并聯諧振（圖2）

 

若沒有電(dian)(dian)容(rong)(rong)C，正(zheng)弦信號u通(tong)過L感應到次級(ji)輸出Uf，Uf電(dian)(dian)壓超前(qian)于u 90°；在L初級(ji)并(bing)聯電(dian)(dian)容(rong)(rong)C，由于電(dian)(dian)容(rong)(rong)對電(dian)(dian)壓的滯后(hou)作(zuo)用，使得L上電(dian)(dian)壓也被強制滯后(hou)90°。因(yin)此，并(bing)聯C后(hou)Uf輸出相位與u相同。

 

3、LC串聯諧振（圖3）

 

對于(yu)輸入正弦信號u，電(dian)(dian)容(rong)C使(shi)得(de)串(chuan)聯回(hui)路(lu)中負載R上的電(dian)(dian)流相(xiang)(xiang)位(wei)超前于(yu)u 90°，電(dian)(dian)感L則使(shi)得(de)同一串(chuan)聯回(hui)路(lu)中的電(dian)(dian)流相(xiang)(xiang)位(wei)再(zai)滯(zhi)后(hou)90°二者相(xiang)(xiang)位(wei)偏移剛好抵(di)消(xiao)。

 

因此(ci)，輸出Uf與(yu)輸入u同相(xiang)。

 

4、總 結：

 

（注意，相位影響不一定都是(shi)90°，與其它部分相關，具體則要計算(suan)）串(chuan)聯電容使得串(chuan)聯支(zhi)路電流相位超前(qian)，從而影響輸(shu)出電壓相位。

 

并(bing)聯(lian)電容(rong)使得(de)并(bing)聯(lian)支路電壓相位滯后，從而(er)影響輸出電壓相位。

 

串(chuan)聯電感使得串(chuan)聯支路電流相位滯后，從而影響輸(shu)出(chu)電壓相位。

 

并(bing)聯電感使得并(bing)聯支路支路電壓超前，從而影響(xiang)輸(shu)出電壓相位。

 

更簡(jian)潔的記憶：電(dian)(dian)(dian)(dian)容使電(dian)(dian)(dian)(dian)流相位超前(qian)(qian)(qian)，電(dian)(dian)(dian)(dian)感使電(dian)(dian)(dian)(dian)壓相位超前(qian)(qian)(qian)。（均(jun)指元件上的電(dian)(dian)(dian)(dian)流或(huo)電(dian)(dian)(dian)(dian)壓）電(dian)(dian)(dian)(dian)容——電(dian)(dian)(dian)(dian)流超前(qian)(qian)(qian)，電(dian)(dian)(dian)(dian)感——電(dian)(dian)(dian)(dian)壓超前(qian)(qian)(qian)。

（來源：網絡，版權歸原作(zuo)者(zhe)）