Since the gain A ≈ ∞, v

  

Operational Amplifiers

  for Basic Electronics

  

http://cktse.eie.polyu.edu.hk/eie209

  by Prof. Michael Tse

  January 2005 Where do we begin?

  We begin with assuming that the op-amp is an ideal element satisfying the following conditions: Output resistance = 0 (perfect output stage) Input resistance = ∞ (perfect input stage) Differential voltage gain = ∞

  v v v v Av i i ± o o i

• – – –
• – Since the gain A ≈ ∞, v ≈ 0 if v is infinite,

  i o

  the two input terminals have same potential if v is infinite

  o

  a “virtual” short-circuit exists between the two input terminals

• –
• + – + – + – + –

  Ω; A

  8

  9

  10

  11

  12

  13

  14

  GBW = 4MHz (gain-bandwidth) SR = 13V/µs

  5 CMRR = 100dB

  =100dB = 10

  VOL

  12

  The 347 IC op-amp

  = 10

  in

  R

  7 Manufacturer listed spec:

  6

  5

  4

  3

  2

  1

  single-ended output The 347 is a Quad JFET input op-amp using biFET technology.

  output stage

  V+ V– The basics

  An op-amp is a very high gain differential amplifier. In almost all applications (except in comparator and Schmitt trigger), feedback is used to stabilize the gain.

TWO GOLDEN RULES:

  RULE 1:

  attempts

  The output to do whatever is necessary to make the voltage difference between the two inputs zero.

  RULE 2: The inputs draw no current. Example

  Consider the following op-amp circuit. What is the voltage gain?

  R

2 Apply the Golden Rules:

  i _x R

  1

  0V try

  It first says that the output will to set

• – v _i i
_x

  itself in order to make the difference

  

v

_o it

  between the inputs zero. That means,

• will try to make the –ve input 0 V because the +ve input is 0 V.

  Then, it says that the current flowing into the inputs are zero.

  Therefore, This is the inverting amplifier. Warnings

  The Golden rules sometimes do not apply. NOTE CAREFULLY that Golden Rule 1 says that “the output attempts to…”. The output attempts, but it may fail to do what it wants to do!

  Do Golden rules apply in the following circuits?

• – –
• – +
• – +
• –1V
• – +
• – + sq.

  2 x x Other examples (where Golden rules work) R

2 Applying the Golden rules, we get

  R

  1

• – +

  v _i This is the non-inverting amplifier.

  Here, simply

• – v
_o This is the voltage follower
• v _i
Other examples (where Golden rules work)

  More examples

  R f

  R ₁ v

1 R

  ₂ v

• – 2

  R ₃ v

  3

• This is the summing amplifier.

  R

2 R

  ₁

• – v

  1 R _{1 o} v v

• 2

  R ₂ This is the difference amplifier. Other examples (where Golden rules work)

  More examples

  C R v

• – i
• This is the integrator.

  R C

• – v _i

  v _o

• This is the differentiator (theoretically). In practice, this circuit won’t work!!!
• – ^out

  Examples (where Golden rules do not work)

  2

  by more than 0.0001 V, the output will swing to –10 V.

  1

  is larger than v

  2

  2. If v

  by more than 0.0001 V, the output will swing to +10 V.

  is larger than v

  v

  1

  1. If v

  Since the voltage gain typically exceeds 100,000, the inputs must be within a fraction of a millivolt in order to prevent the output from swinging all the way to extreme positive or negative. It is assumed that the supply voltages are +10 V and –10 V and that the gain is 100,000.

  Comparator

  2 v

  1 v

  The output cannot make the two inputs equal!!! Golden Rule 1 fails!!! Examples (where Golden rules do not work) Comparator

  The output cannot make

  v

• 1

  the two inputs equal!!!

  v _out

  Golden Rule 1 fails!!!

  v

• – 2

  But this simple comparator suffers from a problem if the input signals have noise! The output may switch (jump up and down) when the signals are close to each other.

  Examples (where Golden rules do not work) v

  1 Comparator v

  5V

  2 v

• t

  1 v _out v

• – 2

  v out

  ±

  5V Suppose v = 5V (constant) and v is an input.

  2

  1 This circuit is supposed to compare v with 5V.

  1 But if v has noise, the output may jump when v is near 5V.

  2

  2 Examples (where Golden rules do not work) Schmitt Trigger — a better comparator

  How does it work? ^v _{in v out}

• – + A
_R Assume the op-amp is powered by ₂ ±10V, and now v = +10V. _R out

  Obviously, v must be less than v : _{A 1}

  in

  10R ₁

  v _{in A} < = v R ₁ + R ₂ What happens if v moves just above in

  10R /(R +R )? Clearly, v falls to

  1

  1 2 out –10V because of comparator action.

  Therefore, v drops to –10R /(R +R ), _A

  1

  1

  2

  and v must be greater than v : _A

  in

• –10R
₁

  v _{in A} > = v R ₁ + R ₂ Examples (where Golden rules do not work) Schmitt Trigger

• – + ^{out v}
• R
• –10R
• R

  R ₁ ^{R 2 v in} A We have a situation similar to hysteresis.

  upper trip point =

  10R

  1 R

  1

  2

  lower trip point =

  1 R

  1

  2 t t

• ^{+10 v in v out} _–10

^10R

^{1 R + R 1 2}

^10R

^{1 R + R 1 2 –}

  Examples (where Golden rules do not work) Schmitt Trigger

  10V ^v _{in v out}

• – + _–10V
_90k What are the upper and lower trip points? _10k W _{– 8V +} W Practical considerations Finite input currents

  Very small currents are in fact needed to bias the op-amp input stage. Circuits that have no DC path to inputs won’t work! None of these works!

  C

• – –

  v _i v _i v _o v _o x x

  C Practical considerations Offset in integrator

  The op-amp integrator is very easily saturated if there is a small lack of symmetry in the input signals. This is because the error gets integrated quickly and the output will soon move towards the maximum voltage.

  v _i C

• – +

  C

  In practice we need a discharge path to prevent saturation. Usually R has to be big enough, so that the discharge rate becomes insignificantly slow compared to the signal frequency.

  R

• – +
Applications Current source We see that v is fixed by the voltage divider. _R

  The op-amp will make sure that the voltage across

  R is also equal to v , which is fixed! ₊ v _{R R –}

  Therefore the current flowing down R must be

  LOAD

  I _o R

  which is the load current. Thus, this circuit provide a constant current source for the load.

  Note: the load is floating for this case! Applications Current source for grounded load Again v is fixed by the voltage divider. _R

  V _cc R

  The op-amp will make sure that the voltage at the _– lower end of R is also equal to v , which is fixed! _{R +} Therefore the current flowing down R must be

  v _R

  I _o LOAD

  which is very close to the load current (if base current is small and op-amp draws very small current). Thus, this circuit provide a constant current source for the grounded load. Applications Current source for grounded load

  (voltage controllable) Here, v is controllable/adjustable by v . _{R IN}

  V _cc R

  The current flowing down R, which is close to the

  R ₂

• _– load current I , must be
_o
• ₊ I _x

  V I _{cc cc x} - (V - R ) ₂ I _o = v _R

  R v _{IN +}

  I _o R v _{2 – IN}

  = LOAD R R ₁ R ₁ Thus, this circuit provide a controllable constant current source for the grounded load.

  Other non-ideal behaviour Example of input bias current

  Problem: Since i flows into _b R

  2

  both inputs, the negative input side will have a slightly negative

  R

  1

  dc voltage even when v = 0, ⁱ

• – v _i

  i _b v whereas the positive input side is _o

• still 0V because there is no

  i _b

  resistor there! Therefore, v ≠ 0, _i i.e., some unwanted offset !

  R

  2 R

  1

• – v

  _i

  i Practical solution: _b v _o

• i _b

  R

  ||R

  1

  2 Other non-ideal behaviour Input offset voltage

  Due to imperfect symmetry, some voltage has to be applied to the input to get the output to zero. Typical value ≈ 5 mV.

  The input offset voltage is a function of temperature (due to temperature drift of device parameters).

  Practical solution: In many applications, the dc gain is not needed. We can simply drop the dc gain to 1.

• For example, for the non-inverting amplifier, if we set
• – R

  = 2kΩ

1 C

  = 4.7µF

  1 R R

  2

  1 the cutoff frequency is approx 17 Hz. C

  1 Summary We have studied the basics of op-amps, and some applications.

  Basic rules of op-amp circuit analysis Some practical considerations Some applications