Comparators V S+ v i. v o. Slope = G. R 1 R 2

Transcription

1 Comparators V S V L Slope G. V S R 1 R 2 V L Non-inverting amp. G 1R 2 /R 1. If the op amp has rail-to-rail outputs, then V L V S and V L V S. V S V S R 1 R 2 EE 230 comparators 1

2 X V L V L X For amplifier applications, we try to stay within the linear gain region and avoid operating in the saturated areas. This makes a good amplifier. V L V L But the saturation regions are not totally useless. For example, if the output is saturated at V L, then we know that the input must be large(ish) and positive. Or, if the output is saturated at V L, then we know that the input is large(ish) and negative. Saturated outputs give some comparative information the input is either positive or negative. EE 230 comparators 2

3 Using the saturated levels gives us a yes/no type of circuit. Is the input voltage high? Yes or no? Is the input voltage low? Yes or no? The weakness of using a regular feedback amplifier circuit in this way is the gain region is indeterminate. If the input voltage is such that amplifier is working in its linear region, then the answer to our simple question is Dunno. To make the circuit be more decisive, we should sharpen the gain region transition. This suggests a very simple alternative remove the feedback loop and use the op amp open loop. With its very high openloop gain, there will be an extremely sharp transition from being saturated at the low level to being saturated at the high level. V S V L We can call this a comparator. V S V L EE 230 comparators 3

4 Non-inverting comparator V S V S V S V S V L V L V L V L If > 0, V L if < 0, V L. It s that simple. Shift the comparison point: If >, V L if <, V L. EE 230 comparators 4

5 V S V S R 1 R2 V L V S V S V L Use a voltage divider. (Can be a potentiometer.) V S R 2 R 1 R 2 (V S V S ) Single-supply version. V S R 1 R2 V S V L R 2 V S R 1 R 2 EE 230 comparators 5

6 Inverting comparator Switch the inputs to have it work in the opposite fashion. V L V S V S V L If >, V S if <, V S. EE 230 comparators 6

7 Use positive feedback to improve performance Simple open-loop comparators have problem with chatter. If input signal is noisy and it is close to, the output can bounce back and forth. This is not desirable. We can limit this problem by using positive feedback to introduce hysteresis. Positive feedback also make the output switch even faster from one level to the other. R a Looks normal enough. But wait, the feedback loop is backwards. This is a positive feedback loop. In that case v v. If changes, it causes v to change. When v crosses v ( ), output will change. Extremely non-linear. Have to analyze it piecemeal. EE 230 comparators 7

8 Start by assuming that vi is positive enough to have v > VREF. Then vo VL. R b Write a node equation at the non-inverting input. vi v v v vi VL VREF vi 1 vo VL VL As long as v > VREF, the output will stay high. If we start decreasing vi, v will decrease correspondingly. If vi drops far enough, then v will become less than VREF, and the output will switch from high to low. We can find the input voltage at which the switch occurs. VREF EE 230 VTL 1 VL VTL VREF 1 VL comparators 8

9 V L R a V TL V L V TL 1 R a R a V L As moves from high to low, the output will switch from high to low, as expected, and the switch occurs when the input voltage crosses V TL. EE 230 comparators 9

10 Now consider the opposite case assume that vi is negative enough to have v < VREF. Then vo VL. vi v v v vi VL vi VREF 1 VL vo VL If we start increasing vi, v will increase correspondingly. If vi increases enough, then v will become greater than VREF, and the output will switch from low to high. We can find the input voltage at which the low-to-high switch occurs. VREF EE 230 VTH 1 VL VTH VREF 1 VL comparators 10

11 R a V L V TH V L- V TH 1 R a As moves from high to low, the output will switch from high to low, as expected, and the switch occurs when the input voltage crosses V TH. R a V L Put the two together. V TL V L V TH Since the up and down transitions occur at different voltages, the circuit exhibits hysteresis. V L- Hysteresis: ΔV T V TH V TL R a (V L V L ) EE 230 comparators 11

12 Inverting comparator with positive feedback The same kind of thing can be done with the inverting comparator. Using positive feedback will introduce hysteresis into the transfer characteristic. R a When is low, the output is high, V L. As increases, at some point it becomes bigger than v and the output will go low. So we need to know the value of v when the output is high. Writing the node equation at the non-inverting terminal, v R a v Solve for v with V L. v R a V L 1 R a This is voltage at which the input will switch from high to low. EE 230 comparators 12

13 V L V TH R a V L 1 R a V TH V L- Going the other way, when is high, the output is low, V L. As decreases, at some point it becomes smaller than v and the output will go high. So we need to know the value of v when the output is low. Again, writing the node equation, Solving for v with V L. v R a V L 1 R a This is the input voltage at which the input will switch from low to high. EE 230 comparators 13

14 V L V TL R a V L 1 R a V TL V L V L Put the two together. V TL V L V TH Hysteresis: ΔV T V TH V TL R a (V L V L ) 1 R V L V L a 1 R a EE 230 comparators 14

15 Example 22 k! Find VTL and VTH for the non-inverting comparator shown. Also calculate the hysteresis width for the comparator. vi The op-amp has high and low output limits of VL 7.5 V and VL 7.5 V. VTL VREF <latexit sha1_base64"3n/5g/dbqfviq/fzg2r2ze/eww0">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</latexit> 1 10 kω (1 V) 1 22 kω VTH VREF <latexit sha1_base64"yneagwgb2l45oxuokjyc59lga">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</latexit> 1 10 kω (1 V) 1 22 kω <latexit sha1_base64"ooywu9xdnzozqic3jiqfyfoiqm">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</latexit> EE 230 ΔV (VL <latexit sha1_base64"ky/n4glevgsj24sto0nxkg24x0u">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</latexit> 10 k! VREF 1V vo VL 10 kω 22 kω <latexit sha1_base64"esucgzbr/hoqg4vdlsmw8ltv0e4">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</latexit> (7.5 V) 1.95 V VL 10 kω 22 kω ( 7.5 V) 4.86 V VL ) 6.81 V comparators 15

16 Example 3.3 k! Find VTL and VTH for the inverting comparator shown. Also calculate the hysteresis width for the comparator. The op-amp works with a single supply and has high and low output limits of VL 6 V and VL 0 V. VTL VREF 1 <latexit sha1_base64"8qliumxyidf/mjsr1g2jm5fkgzy">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</latexit> VTH <latexit sha1_base64"ih1vsi2itlob640u8ylljo7ulhq">aaacrnicbzhbahsxeibl7sl1t0572rtru0hjmluh0bzampsui1y4iy4d9rjo5vlbwcst0myjexqdpk1vwjbvgu7edsd0plr0fszkxeswexjv0olu379y9t3e//edho8dpovtpl6yudych11kby5xzkelbeavkukwmsdkxmmoxhxt/9b2mfvqd47kctgqzjqrbgqaudfoxmts/8fqdnrsgcre2z5/mp17ixjpnxyh/dpofcu2tv81ungvxgv9kzinqjlnjhi9lujyvtzugsfxdjrx0lcyeqyqcelpaktlaxvmazgaepwak2datspx0zyjqw2oslkk7o9rooldyuyzxklgzndtdr4p8cy3f29qjvduiiq8fkmpjudomb3qqdhcuyyaynyl8kvzfnqbobtbr6zurobvvekuaiw4nsiolxifhgvoausmvfovgzazxqp0pxzua/jbjzetai9og/poqwfyvlqw2w6jshybf1mmj3vvesm319381m9shz8oickis8ix1yqgzksdj5qx6sxr3lesjki2ydwru2px5rryimv8fz9byqq</latexit> VREF 1 VL VL VL VL ΔV 1 Ra <latexit sha1_base64"xvnqijuvwi2iew9dzptgngoowis">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</latexit> EE V 1 <latexit sha1_base64"cgdm1dnykhldmycn8b4y6kwvdhi">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</latexit> <latexit sha1_base64"lx4rp2upks4je/bn8jbbuiccby">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</latexit> 2.5 V k! VREF 2.5 V 3.3 kω 3.3 kω 3.3 kω 3.3 kω (0 V) 3.3 kω 3.3 kω 3.3 kω 3.3 kω (6 V) vi vo 1.25 V 4.25 V 6V 0 3V 3.3 kω kω comparators 16

17 Example Design the non-inverting comparator shown at right so that it has VTL 2.0 V and VTH 4.0 V vi The op-amp has high and low output limits of VL 6 V and VL 0. VTH VREF <latexit sha1_base64"yneagwgb2l45oxuokjyc59lga">aaacv3icbvhbattaef2rt9s9oe1jx5aygkmti5vcw2gg9jy85mejcrywjbitr/bi1ursjkkm0hf1w/rq1/y3urjdij0m7hi4z2z250yck2nj9381vhv3hzx8tpw4etpscvwtsvl2xwgif9kanmxmzguumnfzkk8di3cgmscbdpvtb64aqnlzkp3mooxqmwizsadkqap1erox5ccupuann339uockeoshbmdegyrmiknffvwjkzeq70v5btf1onmvolbb7/ql4ldbsajttopetn0yhonmfclqegqshqztqmsdemhsgqghcucxawmohrqq4p2vc5mr/gbx4x5khl3npefe7oihntaerq7zbroaje1mrxlgxaufbyvuucfolh5jcccp4bsqfs4oc1nwbeea6v3ixbeclobvxxln0zlgstvjef1qkbiwbrkjrmubii5sc1pvuzqu25fo/toux813vsmjjlt3uot7rwzxtnsjtlwewwafxv033u/dypt93dz6udblhxbid1wmasen2zhqszwt7yx6zpyv98wbetrll6ley1xziq2fn/8hurleqw</latexit> VTL VREF <latexit sha1_base64"3n/5g/dbqfviq/fzg2r2ze/eww0">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</latexit> VREF 1 VL 1 VL vo Subtracting the bottom equation from the top gives: VTH VTL <latexit sha1_base64"qcdnouc8w84oerzsfiwflewmngc">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</latexit> (VL VL ) <latexit sha1_base64"c//q6ttrcxxljqkrppmilpifgm">aaac2nicbzhpb9mwfmed8guux904crgojg2xvsk6wzbamgqso/rq0npoaqpidv86q44t2sovzqtj8svv4wb/wlh7lawtenjsb7fj/tvpfgurqggcx596fefuvz37tqcphz1ut/d65us0bx6pjozvhgza1io6kfacre5bpaojqzgs/foh3wbbusmzngrq5syqrkj4awtiutylgjgy88xqxrxnf3dex6cxlvjxdp1nvbtl5wdemdajzxeudjxdmwnkm4/lary1zw2yugr3w7h9ubqcpzbb4pwlrpkhd141xumjhkvuldijtnmgay5rixtklieqjyqdosmz9guhlyqlokjymvbkrpvyyqmmbapqrqk13euldvmkdqi91ogl2bbc/b/3rda5cqqhcolbmvxfywfpjhr12m6ero4youvjgth/5xys2a7hxysg7csz86bb1rszgsledablspxjppzaabtjpsrquwyauepsr/ynuf4wqcxfwgoo848/kgbziu5dbskmltxt8uvapwm1b46bhxny9kx3yjdwnbyqkr8kposnd0ioc/cs/pc/z/cj/6n/zv69sfw95ynzcp/hh8y05xk</latexit> VTH VL VTL 4V 2V VL 6V Choose a pair resistors with this ratio. Then, using the VTL equation: VREF <latexit sha1_base64"hywww/joxufod/xn64reuoz7cs">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</latexit> EE 230 VL Ra VTL 1 2 V (0.333) (6 V) 3V 1 (0.333) (Using VTH equation would give the same answer.) comparators 17

18 Example Design the inverting comparator shown at right so that it has VTL 1.0 V and VTH 3.0 V VTH <latexit sha1_base64"ih1vsi2itlob640u8ylljo7ulhq">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</latexit> 1 VL VTL VREF 1 <latexit sha1_base64"8qliumxyidf/mjsr1g2jm5fkgzy">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</latexit> Subtracting the right equation from the left one gives: vi VREF The op-amp has high and low output limits of VL 5 V and VL 5 V. VREF VTH Finally, using the VTH equation: <latexit sha1_base64"8jyt7k9k/nu1ehmhmhng6dcvyqm">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</latexit> VL VTH VREF VTH <latexit sha1_base64"/pmstvrrkhv6px7uocn2pakmdye">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</latexit> VTL VL VTL 1 (3 V) ( ) <latexit sha1_base64"3ftejjrlnbxrz1ijb1ztit0pmig">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</latexit> EE 230 vo VL (VL 1 <latexit sha1_base64"kutqhiafuhpmddd0s6pgvozfb6s">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</latexit> After a bit of algebra (note the inversion of the ratio): 5V 1 3V VL ) ( 5 V) ( 1 V) or <latexit sha1_base64"ar0/n30h9x61e30iz1i5m9wdmfi">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</latexit> VL (0.667) (5 V) 1.67 V comparators 18