What is an **amplifier**?

An **amplifier** is a device used to **increase** the **amplitude** or **power** **level** of a **small signal** but **without** **distorting** it

**Passive components** ____ or ____ signal power

**Active components** ____ external power and ____

**Passive components absorb** or

**signal power**

__transfer__**Active components** ** accept** external power and

__amplify__**Passive components** __ ___ need power for them to work

**Active components** __ need power for them to work

**Passive components do not** need power for them to work

**Active components do** need power for them to work

For a voltage amplifier the Gain = ?

Gain = V_{out} / V_{in}

**Gain** is a ____ so has no ____

**Gain** is a ** ratio** so has no

__units__To calculate the voltage delivered to the load we need to know the amplifiers parameters…(3 things)

- Input resistance of amplifier r
_{in} - Output resistance of amplifier r
_{out} - Open circuit voltage gain A
_{v }

If we know the internal resistance of the source R_{s} , then the voltage across the input terminal of amplifier will be…(equation)

What is R_{s}?

The internal resistance of the source

R_{s} and r_{in} form a…?

Voltage divider

What does a **voltage divider** ciruit look like?

- The
**larger**the value of**r**, the_{in}**closer**the value of**V**is to…?_{in} - This is the reason that in practice ___ ____ ____ is always required

- The
**larger**the value of**r**, the closer the value of_{in}**V**is to_{in}__V___{s} - This is the reason that in practice
is always required__high input impedance__

What is the symbol for **open circuit voltage gain** and what is it larger than?

A_{v} - always larger than 1, very, very large!

What is **Open circuit voltage gain**?

It is the voltage gain if the amplifier is not loaded i.e. if R_{L} is replaced with an ∞ resistance

If a load is connected to the amplifier, the voltage across the load is…(equation)

A ____ output resistance is preferred in an amplifier

A ** small** output resistance is preferred in an amplifier

What is IC and give an example

**Intergrated** **circuit** and an **Op amp**

Define **inverting input**

the phase angle of the output will be 180° different from that of the input applied at this terminal.

The ____ ____ is often omitted from circuit diagrams for simplicity, but it must be understood to be present at all times

The __ground__** line** is often omitted from circuit diagrams for simplicity, but it must be understood to be present at all times

A perfect amplifier should have…(5 things)

**High gain****High input impedance**so that any signal could be supplied to it without a loading problem**Low output impedance**so that the power supplied by the amplifier is not limited**Zero gain**for common-mode input signal**Infinite**bandwidth

An ideal **op-amp** should have…(5 things)

- Infinite voltage gain, Av ≈∞
- Infinite input impedance, rin ≈∞
- Zero output impedance, rout ≈0
- Zero input offset voltage (i.e. exactly zero out if zero in)
- Infinite bandwidth

What is the **current golden rule**?

Because rin≈∞, virtually **no current** can flow into input

What is the **voltage golden rule**?

Because V_{out} ≈A_{v}(V_{p}-V_{n}) and A_{v} ≈∞, V_{p}-V_{n} ≈0, i.e. virtually **no voltage difference** between inputs

Comparison between ideal and real op-amps

In a system, the ____ is compared with the desired ____

If there is a difference between the two, ____ is used to drive the output close to its intended value

In a system, the ** output** is compared with the desired

__output__If there is a difference between the two, ** feedback** is used to drive the output close to its intended value

V_{0} in a feedback amplifier = ?

V_{o }= A_{v} x V_{s}

If the feedback amplifier circuit is modified such that a fraction β of the output is fed back into the input, then the new output becomes;

V_{s} = ?

V’_{o} = ?

The new voltage gain Av ’ of the amplifier with feedback…(equation)

If ß A_{v}>>1, then A’_{v} = ?

What is ß?

The feedback fraction

Feedback voltage, V_{n} = ?

G = ? = ? = ?

ß = ?

G is called the ____ ____and also the ____-____ ____ ____. It is almost entirely determined by the ____ ____ and is hardly affected by small changes in ___{_}

G is called the ** feedback fraction** and also the

**. It is almost entirely determined by the**

__closed-loop voltage gain__**and is hardly affected by small changes in**

__feedback circuit__

__A___{v}Op-amp input resistance = ?

In a feedback amplifier, the input resistance = ?

R_{in} = ? and = ?

R_{in} = V_{in} / i_{in} and

In feedback amplifier, V_{s} = ?

β < 1 ?

Feedback Fraction

The “closed-loop gain”, G, of this feedback system = ?

Feedback equation

Ohm’s law = ?

V =IR

KVL = ?

V_{4} - V_{1} - V_{2} - V_{3} = 0

KCL = ?

i_{1} +i_{3} - i_{1} - i_{4} = 0

Current Golden rule = ?

i_{p} = i_{n} = 0

Voltge Golden rule = ?

v_{p} = v_{n}

What is the virtual ground/earth?

When the voltage at a point is almost zero, but it is not connected to ground

A real earth ____ voltage whereas a virtual earth can’t

A real earth ** absorbs** voltage whereas a virtual earth can’t

A minus sign implies that the polarity of incoming voltage is ____, so it’s an ____ ____

A minus sign implies that the polarity of incoming voltage is ** reversed**, so it’s an

__inverting amplifier__If Rs =Rf , then the amplifier has a ____ ____ (=1) and the incoming signal is ____

If Rs =Rf , then the amplifier has a ** unity gain** (=1) and the incoming signal is

__inverted__In an open circuit, the input resistance of the op-amp is…

…infinite

What is this equation called and what is the 1 +Aß called?

**Feedback equation** and the **feedback factor**

For op-amps with high open voltage gain, G = ? = ? = ?

If A is sufficiently high then Aβ…?

If A is sufficiently high then Aβ >> 1

In this circuit, R_{2} and R_{1} form a ____ ____; they define V_{N }as a fraction of ____

In this circuit, R_{2} and R_{1} form a __potential divider**__; they define V_{N }as a fraction of __**V _{out}__

Comparing a general feedback amplifier circuit with a non-inverting feedback amplifier

In an inverting feedback amplifier, the open loop voltage gain, A, is ____ (as opposed to ____ as postulated for an ideal op-amp)

And the voltage golden rule is…

In an inverting feedback amplifier, the open loop voltage gain, A, is ** finite** (as opposed to

**as postulated for an ideal op-amp)**

__infinite__…not fullfilled, i.e. V_{p} does not = V_{n}

For an **ideal Op-amp**

CGR = ?

VGR = ?

In an **op-amp circuit without feedback**, A is given by…(explanation and equation)

…the **ratio** of the **output** **voltage** to the **difference** between the **two** **input** **voltages**

G = V_{out} / V_{in} = - ??? (big equation)

What happens in this equation if A is large?

The denominator reduces to unity as A gets large

The open loop gain of most commercial op-amps is usually higher than __^{_} , therefore the assumption of ideal behaviour of op-amp is ____

The open loop gain of most commercial op-amps is usually higher than ** 10^{4}** , therefore the assumption of ideal behaviour of op-amp is

__acceptable__From ohms law for a real Op-amp??

G is the **closed**-**loop** **voltage** **gain** of the circuit

If **A>>G**

**R _{in} ≈ R_{1}**

The input resistance in an ____ feedback circuit will become ____ if the real op-amp characteristics are taken into account

The input resistance in an ** inverting** feedback circuit will become

**if the real op-amp characteristics are taken into account**

__smaller__In the example of a non-inverting feedback amplifier (lecture 2) we found that ____ negative feedback tends to ____ the input impedance

In the example of a non-inverting feedback amplifier (lecture 2) we found that ** series** negative feedback tends to

**the input impedance**

__increase__A voltage-derived feedback gives rise to a circuit with ____ output resistance

A voltage-derived feedback gives rise to a circuit with ** low** output resistance

When **both** inputs are connected to the **ground** like in this circuit, in an ideal op-amps we expect **V _{out} = 0**, however

**V**. What is this called?

_{out}≠ 0This dc output voltage, when both input terminals are grounded, is called **output offset voltage**

Does an ideal op-amp exist?

What would a typical op-amp display?

The input circuit of an op-amp is a ____ _____ of bipolar transistors (eg. LM741)

The input circuit of an op-amp is a ** symmetrical arrangement** of bipolar transistors (eg. LM741)

Transistors need a small… for correct operation

Transistors need a small ** dc input current, I_{B}**, for correct operation

What is I_{B} ?

I_{B }is called **bias current**

In an op-amp, it is difficult to make two input transistors identical, I_{B} into one input is always ____ from the I_{B} into another

In an op-amp, it is difficult to make two input transistors identical, I_{B} into one input is always ** different** from the I

_{B}into another

I_{B} = ?

The difference in these two currents is defined as ____ ____ (Equation as well)

Its value quantifies the ____ between the input transistors

The difference in these two currents is defined as __offset current__

Its value quantifies the ** mismatch** between the input transistors.

If an adjustable voltage source, V_{os} is connected across the input terminals of a real op-amp:

This external voltage source is adjusted until the output voltage is brought to zero, V_{out}=0

What is the **input offset voltage?**

The **input offset voltage** must exist across the two inputs in order to bring op-amp’s output voltage to ZERO.

What is the **Input Bias Current (I _{B}):**

**Input Bias Current (I _{B}):** the average of the current flowing into both inputs. Typical range: from nA down to pA

What is the **Input offset current (I _{os})**

**Input Offset Current (I _{os}):** the difference of the two input bias currents

What is the **Input Offset Voltage (V _{os})**

Input Offset Voltage (Vos): the voltage that must be applied between two input terminals to set the output voltage to zero. For an ideal op-amp, input offset voltage is zero

When a circuit drives the op-amp output beyond its swing voltage, we say that the op-amp is ____ or “__ ____”

When a circuit drives the op-amp output beyond its swing voltage, we say that the op-amp is ** saturated** or “

**”**

__in saturation__Define **current limit**

**Current limit** indicates the maximum current that an op-amp can deliver to the load

What’s the worst situation in a circuit to do with currents? And how can it be resolved?

**The worst situation**: when the output is **short circuited**

Therefore the **short-circuit current** is used to **define** the **current limit**

Define the **speed limit, - Slew Rate (SR)**

Term used to describe how **fast** the **output** of an op-amp can respond to **changes** in **input voltage**

SR = ?

SR = dv/dt

So for an op-amp to reproduce a sine wave without distortion, its SR needs to be ____ than sine wave’s ____ ____ ____, that is;

So for an op-amp to reproduce a sine wave without distortion, its SR needs to be ** bigger** than sine wave’s

**, that is;**

__maximum change rate__**SR > ωV _{p}**

The **open-loop gain** of an **op-amp** appears in the calculations for

- The voltage gain
- The input impedance
- The output impedance

For most purposes, we assume the ____-____ ____ of an op-amp is very large, this is true at ____ ____ but not so true at ____ ____

For most purposes, we assume the ** open**-

**of an op-amp is very large, this is true at low frequencies but not so true at high frequencies**

__loop gain__How does the op-amp gain depend on the input frequency?

Real Op amps have a frequency dependent open loop gain. Their differential voltage gain tends to decrease as the input frequency increases.

What does a **bode diagram** or **bode plot** represent?

It represents the **response** of a **given component** (or **circuit**) over a **frequency range**

What can be used to **express** the **voltage gain**?

**Decibel (dB)** can be used to express the voltage gain

The gain of most op-amps ____ __ (‘____ __”) at ____ frequencies

The gain of most op-amps ** falls of (“rolls off”)** at

**frequencies**

__high__Define **bandwidth**

**Bandwidth:** freq at which the gain is reduced by a factor of sqrt(2)

(with respect to its value at DC)

What is **“cut-off” frequency** also known as?

**3dB point** or **bandwidth**

Cut-off frequency multiplied by gain is ____ the same value for a specific op-amp

This constant value is called the ____ ____ ____ (___)

Cut-off frequency multiplied by gain is ** always** the same value for a specific op-amp

This constant value is called the __Gain BandWidth Product (GBW)__

What has a higher bandwidth than an open-loop amplifier?

A closed-loop amlifier

Give some limitations of a real op-amp

- Limitated gain bandwidth
- Slew rate

Op-amps perform simple operations such as…

…addition, subtraction, multiplication, differentiation and integration

What does a **differentiator in electronics** do?

The “**differentiator**” in electronics denotes a circuit that performs a mathematical operation (differentiation) on the input voltage

The current flowing through a capacitor, I_{c} , is proportional to the…

The current flowing through a capacitor, I_{c} , is proportional to the rate of voltage change dV/dt and the capacitance C

I_{c} = ?

V_{out }for an ideal op-amp = ?

- The output voltage is the derivative of the input
- Negative sign indicates that the circuit is still an inverter
- RC is known as the “time constant” or, in this circuit, as the “gain factor”

What would V_{out} look like?

V_{out} across the capacitor = ?

- Output voltage is proportional to the integral of the input voltage
- Circuit is an inverter
- Example: Used to integrate the signal from an accelerometer

What can you say about this equation? (3 things)

- Output voltage is proportional to the integral of the input voltage
- Circuit is an inverter
- Example: Used to integrate the signal from an accelerometer

What can you say about this equation? (3 things)

- The output voltage is the derivative of the input
- Negative sign indicates that the circuit is still an inverter
- RC is known as the “time constant” or, in this circuit, as the “gain factor”

Equation for feedback voltage?

V_{f} = *B*V_{out}

Equation for input voltage to the op-amp?

V_{s} = V_{in} - *B*V_{out}