EECS 40/4 Exerimets #6 & #7: The Oeratioal mlifier I. Objective The urose of these exerimets is to itroduce the most imortat of all aalog buildig blocks, the oeratioal amlifier ( o-am for short). This hadout gives a itroductio to these amlifiers ad a smatterig of the various cofiguratios that they ca be used i. art from their most commo use as amlifiers (both ivertig ad o-ivertig), they also fid alicatios as buffers (load isolators), adders & subtractors, itegrators, logarithmic amlifiers, imedace coverters, filters (low-ass, high-ass, bad-ass, bad-reject or otch), ad differetial amlifiers. So let s get set for a fu-filled adveture with o-ams! II. Itroductio: mlifier Circuit efore jumig ito o-ams, let s first go over some amlifier fudametals. amlifier has a iut ort ad a outut ort. ( ort cosists of two termials, oe of which is usually coected to the groud ode.) I a liear amlifier, the outut sigal iut sigal, where is the amlificatio factor or gai. Deedig o the ature of the iut ad outut sigals, we ca have four tyes of amlifier gai: voltage gai (voltage out / voltage i), curret gai (curret out / curret i), trasresistace (voltage out / curret i) ad trascoductace (curret out / voltage i). Sice most o-ams are voltage/voltage amlifiers, we will limit the discussio here to this tye of amlifier. The circuit model of a amlifier is show i Figure (ceter dashed box, with a iut ort ad a outut ort). The iut ort lays a assive role, roducig o voltage of its ow, ad is modelled by a resistive elemet i called the iut resistace. The outut ort is modeled by a deedet voltage source i i series with the outut resistace o, where i is the otetial differece betwee the iut ort termials. Figure shows a comlete amlifier circuit, which cosists of a iut voltage source s i series with the source resistace s, ad a outut load resistace L. From this figure, it ca be see that we have voltage-divider circuits at both the iut ort ad the outut ort of the amlifier. This requires us to re-calculate i ad o wheever a differet source ad/or load is used: i i s s () i L o i o () L S S i INPUT POT i i o OUTPUT POT o L SOUCE MPLIFIE LOD Figure : Circuit model of a amlifier circuit.
EECS 40/4 III. The Oeratioal mlifier: Ideal O-m Model The amlifier model show i Figure is redraw i Figure showig the stadard o-am otatio. o-am is a differetial to sigle-eded amlifier, i.e. it amlifies the voltage differece i at the iut ort ad roduces a voltage o at the outut ort that is refereced to the groud ode of the circuit i which the o-am is used. i i i i i o o i i o Figure : Stadard o-am Figure : Ideal o-am The ideal o-am model was derived to simlify circuit aalysis ad is commoly used by egieers for first-order aroximatio calculatios. The ideal model makes three simlifyig assumtios: Gai is ifiite: () Iut resistace is ifiite: i (4) Outut resistace is zero: o 0 (5) lyig these assumtios to the stadard o-am model results i the ideal o-am model show i Figure. ecause i ad the voltage differece i at the iut ort is fiite, the iut currets are zero for a ideal o-am: i i 0 (6) Hece there is o loadig effect at the iut ort of a ideal o-am: i s (7) I additio, because o 0, there is o loadig effect at the outut ort of a ideal o-am: Fially, because ad o must be fiite, i 0, or o i (8) (9) Note: lthough Equatios -5 costitute the ideal o-am assumtios, Equatios 6 ad 9 are used most ofte i solvig o-am circuits.
EECS 40/4 I i out out i out I i Figure 4a: No-ivertig amlifier Figure 5a: oltage follower Figure 6a: Ivertig amlifier out out out > i i <0 i Figure 4b: oltage trasfer curve Figure 5b: oltage trasfer curve Figure 6b: oltage trasfer curve of o-ivertig amlifier of voltage follower of ivertig amlifier out out out ower ower ower > i i <0 i -ower -ower -ower Figure 4c: ealistic trasfer curve Figure 5c: ealistic trasfer curve Figure 6c: ealistic trasfer curve of o-ivertig amlifier of voltage follower of ivertig amlifier I. No-Ivertig mlifier ideal o-am by itself is ot a very useful device, sice ay fiite o-zero iut sigal would result i ifiite outut. (For a real o-am, the rage of the outut sigal is limited by the ositive ad egative ower-suly voltages.) However, by coectig exteral comoets to the ideal oam, we ca costruct useful amlifier circuits. Figure 4a shows a basic o-am circuit, the o-ivertig amlifier. The triagular block symbol is used to rereset a ideal o-am. The iut termial marked with a (corresodig to ) is called the o-ivertig iut; the iut termial marked with a (corresodig to ) is called the ivertig iut. To uderstad how the o-ivertig amlifier circuit works, we eed to derive a relatioshi betwee the iut voltage i ad the outut voltage out. For a ideal o-am, there is o loadig effect at the iut, so i (0)
EECS 40/4 Sice the curret flowig ito the ivertig iut of a ideal o-am is zero, the curret flowig through is equal to the curret flowig through (by Kirchhoff s Curret Law -- which states that the algebraic sum of currets flowig ito a ode is zero -- to the ivertig iut ode). We ca therefore aly the voltage-divider formula fid : From Equatio 9, we kow that i, so () out out i () The voltage trasfer curve ( out vs. i ) for a o-ivertig amlifier is show i Figure 4b. Notice that the gai ( out / i ) is always greater tha or equal to oe. The secial o-am circuit cofiguratio show i Figure 5a has a gai of, ad is called a voltage follower. This ca be derived from the o-ivertig amlifier by lettig ad 0 i Equatio. The voltage trasfer curve is show i Figure 5b. frequetly asked questio is why the voltage follower is useful, sice it just coies iut sigal to the outut. The reaso is that it isolates the sigal source ad the load. We kow that a sigal source usually has a iteral series resistace ( s i Figure, for examle). Whe it is directly coected to a load, esecially a heavy (small-resistace) load, the outut voltage across the load will degrade (accordig to the voltagedivider formula). With a voltage-follower circuit laced betwee the source ad the load, the sigal source sees a light (high-resistace) load -- the iut resistace of the o-am. t the same time, the load is drive by a owerful drivig source -- the outut of the o-am.. Ivertig mlifier Figure 6a shows aother useful basic o-am circuit, the ivertig amlifier. It is similar to the oivertig circuit show i Figure 4a excet that the iut sigal is alied to the ivertig termial via ad the o-ivertig termial is grouded. Let s derive a relatioshi betwee the iut voltage i ad the outut voltage out. First, sice ad is grouded, 0. Sice the curret flowig ito the ivertig iut of a ideal o-am is zero, the curret flowig through must be equal i magitude ad oosite i directio to the curret flowig through (by Kirchhoff s Curret Law): i out () Sice 0, we have: out i (4) The gai of ivertig amlifier is always egative, as show i Figure 6b. 4
EECS 40/4 5 I. Oeratio Circuit Figure 7 shows a oeratio circuit, which combies the o-ivertig ad ivertig amlifier. Let s derive the relatioshi betwee the iut voltages ad the outut voltage out. We ca start with the o-ivertig iut ode. lyig Kirchhoff s Curret Law, we obtai: (5) lyig Kirchhoff s Curret Law to the ivertig iut ode, we obtai: out (6) Sice (from Equatio 9), we ca combie Equatios 5 ad 6 to get out (7) where ad Thus this circuit adds, ad ad subtracts, ad. Differet coefficiets ca be alied to the iut sigals by adjustig the resistors. If all the resistors have the same value, the ( ) ( ) out (8) out Figure 7: Oeratio circuit
EECS 40/4 II. Itegrator y addig a caacitor i arallel with the feedback resistor i a ivertig amlifier as show i Figure 8, the o-am ca be used to erform itegratio. For examle, a square-wave iut would give a triagular outut wave! simle way to fid out / i is to make. The, out idt C (9). C i out Figure 8: Itegrator III. Differetial mlifier Figure 9 shows the differetial amlifier circuit. s the ame suggests, this o-am cofiguratio amlifies the differece of two iut sigals. out ( ) (0) If the two iut sigals are the same, the outut should be zero, ideally. To quatify the quality of the amlifier, the term Commo Mode ejectio atio (CM) is defied. It is the ratio of the outut voltage corresodig to the differece of the two iut sigals to the outut voltage corresodig to commo art of the two sigals. good o-am has a high CM. - 0-0 out Figure 9: Differetial amlifier 6
EECS 40/4 IX. Frequecy esose of O-m The frequecy resose of ay circuit is the grah of the magitude of the gai i decibels (d) as a fuctio of the frequecy of the iut sigal. The decibel is a commo uit of measuremet for the relative loudess of a soud or, i electroics, for the relative differece betwee two ower levels. ( decibel is oe-teth of a "el", a seldom-used uit amed for lexader Graham ell, ivetor of the telehoe.) The gai exressed i d is 0 log 0 G. The frequecy resose of a o-am is a low ass characteristic (i.e. assig low-frequecy sigals, atteuatig high-frequecy sigals) as show i Figure 0. Gai (log scale) - d oit Freq (Hz) Figure 0: Frequecy resose of o-am. The badwidth is the frequecy at which the ower of the outut sigal is reduced to half that of the maximum outut ower. This occurs whe the gai dros by d. I Figure 0, the badwidth is Hz. For all o-ams, the Gai*adwidth roduct is a costat. Hece, if the gai of a o-am is decreased, its oeratioal badwidth icreases roortioally. This is a imortat trade-off cosideratio i o-am circuit desig. I Sectios III through III above, we assumed that the oam has ifiite badwidth. X. More o O-ms ll of the above circuits have oe thig i commo. There exists a ath from the outut of the oam to its ivertig iut termial. The egative feedback esures that the o-am oerates i the liear regio (as oosed to the saturatio regio, where the outut voltage is saturated at oe of the ower-suly voltage levels). mlificatio, additio ad subtractio are liear oeratios. Note that ay DC offset i the iut sigal(s) is icluded i these oeratios, uless we add a caacitor i series with the iut sigal(s) to block the DC comoet(s). XI. The LM74 Oeratio mlifier The LM74 is a famous biolar-trasistor-based oeratioal amlifier. comariso of ideal oam ad LM74 characteristics give i Table I leads to the followig guidelies for usage: Two ower-suly voltages (oe ositive, oe egative) must be coected to the LM74. The iut voltage should fall withi the rage betwee the two ower-suly voltages. The ower-suly voltages limit the outut voltage swig. The voltage-trasfer characteristics of the o-ivertig amlifier, the voltage follower ad the ivertig amlifier are illustrated i Figures 4c, 5b ad 5c, resectively. The outut swig also deeds o the load resistor L. I order for the LM74 to work like a ideal o-am, do t coect too 7
EECS 40/4 heavy a load (resistor of low resistace) to it. s show i Table I, the maximum curret it ca outut is about 5 m. void cotiuous oeratio uder maximum curret outut; otherwise it ca bur your figer! The iut resistace of the LM74 is ot tremedously large, so resistors like ad show i Figure 4 ad 6 should ot be too large. Of course they should ot be too small, sice either the exteral sigal source or the LM74 itself may have sufficiet curret drivig caacity. You ca refer to electroic hadbooks for more detailed erformace arameters of LM74. Table I Comariso of ideal o-am ad LM74 Parameter Ideal OP- LM74 MP Gai 00,000 i ~6MΩ Ii 0 0~80µ i age No limit ±5 (Power suly ±5) out Swig No limit ± (L>0KΩ), ±0 (L>KΩ) Iout max No limit 5m adwidth.5mhz Power suly max ± Power Suly OUT 8 7 6 5 LM74 4 Power Suly - Figure : Piout diagram for the LM74 LM74 is: The o-am is ackaged i a eoxy mii-dip ( dual ilie ackage ) which has 4 is emergig from each of the two sides of the ackage. The most imortat art of the idetificatio is to ote that Pi is marked by a small circular idetatio i the lower left-had corer of the ackage whe viewed from the to side with the maufacturer s markig readig uright. The i umbers o ICs always start with Pi beig this labeled i ad icrease couter-clockwise as read from the to side of the ackage. Thus o this articular ackage, Pi 8 is directly across from Pi, ad Pi 5 is diagoally across from Pi. You will eed to use oly 5 of the 8 is. These are: Ivertig Iut Pi, No-Ivertig Iut Pi, Negative Suly Pi4, Outut Pi6 ad Positive Suly Pi7. Other is are available for a otioal offset ull adjustmet (Pis & 5), which is uecessary for the circuits used i this exerimet. Do ot groud these is, as this will result i failure of the o-am. Pi 8 has o iteral coectio ito the silico chi iside. 8