Notes on Operational Amplifiers (Op Amps).

Transcription

1 Phys303 L.. Bumm [ver.] Op mps (p) Notes on Operational mpliiers (Op mps). omments. The name Op mp comes rom operational ampliier. Op mp Golen ules (memorize these rules) ) The op amp has ite open-loop ga. ) The put impeance o the / puts is ite. (The puts are ieal voltmeters). The put impeance is zero. (The put is an ieal voltage source.) 3) No current lows to the / puts o the op amp. This is really a restatement o golen rule. 4) n a circuit with negative eeback, the put o the op amp will try to ajust its put so that the voltage ierence between the an puts is zero ( ). DEL OP MP BEHO. The relationship between the put ant the put o an ieal op amp (assumptions: ite open loop ga, unlimite voltage). or > 0 : or < 0 : or 0 : 0 Op mp Schematic Symbol (The upper put is usually the vertg put. Occasionally it is rawn with the non-vertg put on top when it makes the schematic easier to rea. The position o the puts may vary with the same schematic, so always look closely at the schematic! ) Negative Feeback. Most o the basic op amp builg blocks rely on negative eeback. You can easily ientiy the type o eeback use by the op amp circuit. For negative eeback, the put is connecte to the vertg put ( put). For positive eeback, the put is connecte to the non-vertg put ( put). The nput mpeance o the ircuit is ee as the rate o change o with respect to a change o. This is simply the erivative. The put impeance o the circuit is not general the same as the impeance o the op amps puts. The Output mpeance o the ircuit, or the examples shown here, is the put impeance o the op amp. Output impeance is ee as the rate o change o with respect to a change o. This is simply the erivative. For the ieal op amp, the put impeance is zero.

2 Phys303 L.. Bumm [ver.] Op mps (p) Basic Op mp Builg Blocks nvertg mpliier nalysis o the vertg ampliier starts with our op amp golen rules. From rule #4 we know that an that 0 because is connecte to groun. From rule #3 we know that because no current lows to the vertg put. 0 Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL). 0 0 The voltage ga is the erivative o with respect to. When the ampliier has only one put an 0 when 0, we will make the assumption that /. v lternatively we coul have starte our analysis rom the voltage ivier orme by an. The voltage ivier will relate the voltage at with an. n this case The total voltage across the ivier is. Because the bottom en o the ivier is not connecte to groun, we must a the extra term to oset. We arrive at the same result.

3 Phys303 L.. Bumm [ver.] Op mps (p3) ( ) 0 The put impeance o the vertg ampliier is eterme by. Note that is hel at the same voltage as by the op amp eeback. Because is connecte to groun, the put impeance is just. Non-vertg mpliier

4 Phys303 L.. Bumm [ver.] Op mps (p4) nalysis o the non-vertg ampliier starts with our op amp golen rules. From rule #4 we know that an that because is connecte to. From rule #3 we know that because no current lows to the vertg put. Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL). The voltage ga is the erivative o with respect to. When the ampliier has only one put an 0 when 0, we will make the assumption that /. v lternatively we coul have starte analysis rom the voltage ivier orme by an. The voltage ivier will relate the voltage at with an. n this case The total voltage across the ivier is an the we know that. We arrive at the same result.

5 Phys303 L.. Bumm [ver.] Op mps (p5) The put impeance o the ollower is the put impeance o the op amps put. For an ieal op amp the put impeance is ite. oltage Follower This is a special case o the non-vertg ampliier with an 0. The ollower has a very high put impeance. oltage ollower has application when the source voltage can not supply very much current, a ph meter or example. urrent-to-oltage onverter (K, - onverter, Transimpeance mpliier). This circuit takes an put current an converts it to an put voltage. The put impeance o the ieal current to voltage converter is zero (the ieal current meter). 0 nalysis o the current-to-voltage converter starts with our op amp golen rules. From rule #4 we know that an that 0 because is connecte to groun. From rule #3 we know that because no current lows to the vertg put. 0 Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL). 0 The current-to-voltage converter has transimpeance ga. Transimpeance ga is not unitless, it has units o impeance (Ohms). The transimpeance ga is the erivative

6 Phys303 L.. Bumm [ver.] Op mps (p6) o with respect to. When the ampliier has only one put an 0 when 0, we will make the assumption that /. Summg mpliier. This circuit will a (an subtract) the put voltages. Subtraction is accomplishe by vertg the voltages beore ag them. Note that summg can only occur or puts to the vertg sie o the op amp. This is because o the noe is a current summg junction where the put currents sum to the eeback current. Th 3 3 L the ga o the nth put : n n n the impeance o the nth put : n n n n This is another look at the summg ampliier that emphases the summg junction. nalysis o the summg ampliier starts with our op amp golen rules. From rule #4 we know that an that 0 because is connecte to groun. From rule #3 we know that n because no current lows to the vertg put. ( n is the current o the nth put.) 0 n 3 Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL).

7 Phys303 L.. Bumm [ver.] Op mps (p7) n n n n 0 n n n n n n n 0 ( ) The voltage ga is the erivative o with respect to. 3 3 L the ga o the nth put : n n n Dierential mpliier. The term ierential is use the sense o ierence. Do not conuse the ierential ampliier with the ierentiator. One important application o the ierential ampliier over comes the problem o groung that you encountere lab when usg the oscilloscope to make measurements. The typical oscilloscope always perorms voltage measurements with respect to is own groun. ierential ampliier use beore the scope put coul measure the with respect to. The groun o the ierential ampliier woul be connecte to the groun o the scope or this application, so the will be measure correctly. ( ) the ga or : the ga or : nalysis o the ierential ampliier starts with our op amp golen rules. From rule #4 we know that. From rule #3 we know that an that 3 4 because no current lows to the puts. 3 4

8 Phys303 L.. Bumm [ver.] Op mps (p8) Then we can the relationship between,, an usg the voltage ivier equations. We recognize that an that will be the put o the voltage ivier orme by the two resistors connecte to the non-vertg put. The voltage at is the put o the voltage ivier orme by the two resistors connecte to the vertg put. ( ) ( ) ( )

9 Phys303 L.. Bumm [ver.] Op mps (p9) The voltage ga is the erivative o with respect to each put. the ga or : the ga or : The vertg ampliier with generalize impeances. The results erive above can be extene to general impeances. Note that an can be the impeance o any network. The ollowg are examples o the vertg ampliier, but NY o the previous examples can be generalize this way. ntegrator. capacitor as the eeback impeance. j ω ω ( t) ( t) t j ω ω

10 Phys303 L.. Bumm [ver.] Op mps (p0) nalysis o the tegrator the requency oma is a simple extension o our generalize result or the vertg ampliier. jω jω jω j ω j ω ω Time Doma nalysis o the ntegrator starts with our op amp golen rules. From rule #4 we know that an that 0 because is connecte to groun. From rule #3 we know that because no current lows to the vertg put. 0 Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL). 0 t t ( ) ( 0 ) t t t t t t

11 Phys303 L.. Bumm [ver.] Op mps (p) Dierentiator. capacitor as the put impeance. jω ω ( t) ( t) t jω ω nalysis o the ierentiator the requency oma is a simple extension o our generalize result or the vertg ampliier. jω jω jω jω ω jω ω Time Doma nalysis o the Dierentiator starts with our op amp golen rules. From rule #4 we know that an that 0 because is connecte to groun. From rule #3 we know that because no current lows to the vertg put. 0 Then we can the relationship between an usg Ohm s law (OL) an Kirchho s voltage law (KL).

12 Phys303 L.. Bumm [ver.] Op mps (p) t ( ) t t 0 t t t

13 Phys303 L.. Bumm [ver.] Op mps (p3) The General Op mp ircuit Example: an op amp circuit with 3 vertg an 3 non-vertg puts What can we say ab such a complicate lookg ampliier? Don t panic, we can use what we have learne rom the above analyses to palessly arrive at the solution. With og any analysis, what can we say? First, we know that 3 the ga o the nth put : 3 n 4 4 Secon, we know that the voltage gas or,, an 3 will be vertg (negative) an that the voltage gas or 4, 5, an 6 will be non-vertg (positive). We coul simply blaze away at the problem by applyg the op amp golen rules just like we i or the erivations or the basic op amp builg blocks, but there is a better way. The Strategy. We will make use o the results or the basic op amp builg blocks an the prciple o superposition (e.g. the vertg ampliier an the non-vertg ampliier). To apply the prciple o super position, we analyze the ga or one put at a time an turn o all the other puts (set them to zero). We treat each put as an ieal voltage source, so that an put that is turne o is equivalent to a connectg the put termal irectly to groun. The vertg puts an the non-vertg puts will behave ierently. nalysis o the nvertg nputs by Superposition Let s irst use analyze the voltage ga o the put. We procee by connectg all the other puts to groun. (nalysis o the voltage ga or the other vertg puts (v an v 3 ) is analogous.) n

14 Phys303 L.. Bumm [ver.] Op mps (p4) This simpliies to: Notice that the non-vertg put, is connecte to groun though a resistor. Because no current lows to the op amp s puts, 0, equivalent to it beg connecte irectly to groun (see below). This looks like a summg ampliier with 3 0. The result or the summg 7 ampliier is. We can o the same analysis or each vertg put. (Why

15 Phys303 L.. Bumm [ver.] Op mps (p5) on t the two resistors an 3 enter this analysis or? Ht: onsier the voltage across these two resistors.) nalysis o the Non-nvertg nputs by Superposition Now let s use analyze the voltage ga 4 o the non-vertg put 4. We procee by connectg all the other puts to groun. (nalysis o the voltage ga or the other nonvertg puts (v 5 an v 6 ) is analogous.) This simpliies to: This is a non-vertg ampliier. The resistors on the non-vertg sie, 4, 5, 6, an 8, orm a voltage ivier that reuces the voltage seen by. t is the voltage at that is seen by the op amp. The voltage ga o is eterme by the resistors on the vertg sie,,, 3, an 7. Hence the voltage ga 4 o the 4 put has a term rom the voltage ivier, relatg 4 to, an a term or the voltage ga o, relatg to. The voltage ga 4 is the prouct o the two term an relates 4 to

16 Phys303 L.. Bumm [ver.] Op mps (p6) The voltage gas or the other non-vertg puts can be oun this way. n important observation is that multiple puts to the non-vertg sie o the op amp o not sum the simple way that they o or vertg puts. Thus the summg ampliier that we liste as a basic builg block oes not have a non-vertg analog! ( we nee a non-verte sum, we just ollow the summg ampliier with a unity ga vertg ampliier.)