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Chapter 1: Signals and Amplifiers

• [[#1.1 Signals and Sources]]
• [[#1.2 Frequency Spectrum of Signals]]
• [[#1.3 Analog and Digital Signals]]
• [[#1.4 Amplifiers]]
• [[#1.5 Circuit Models for Amplifiers]]
  [[#Chapter 2 Operational Amplifiers]]

1.1 Signals and Sources

Alternating Current (AC) is a time varying, sinusoidal signal.

e.g. Microphone

Direct Current (DC) is a static or fixed signal.

e.g. Battery

Recap: Relating Signals to Thevenin and Norton Equivalent Circuits

Let's think of a signal source as a "black box"

• It doesn't matter so much what is inside the box, but rather how it behaves outside the box.
• Has two terminals coming out of it, which shows us:
  1. Voltage
  2. Current coming in/out
• We connect this to a "load"
  • Analogous to what you do with Thevenin/Norton; separating the "load" (usually a resistor) from the source (the Thevenin/Norton simplification).

1.2 Frequency Spectrum of Signals

I don't think we're doing much of this at all in this course?

1.3 Analog and Digital Signals

"analog" like a physical voice, whereas "digital" is like the .mp4 file of a voice - stored as binary.

1.4 Amplifiers

Amplification is when a signal comes into a circuit and gets increased ("amplified"). Often we simplify this to a single triangle.

In the above image, the reference voltage is set to ground, i.e., $V=0$. So, $V_o$ and $V_i$ are in reference to the ground.

Linear amplifier

A linear amplifier is an amplifier that amplifies linear, which is to say that the output voltage follows this equation:

$A_v$ in this case is a single, unchanging constant. So, $v_o(t)$ gets scaled by some factor $A_v$ always. This value of $A_v$ is known as the voltage gain.

1.5 Circuit Models for Amplifiers

"Direct extension of Thevenin's and Norton's" - Phang

Modelling a Linear Amplifier with Thevenin's Theorem

Given a "black box" circuit (i.e., one that has a source connected to a load), we can model it using Thevenin's Theorem, as long as it is linear. Thus, we can also model a linear amplifier using a Thevenin circuit.

The input side of the amplifier can be modelled as a resistor (since it is a linear input), which comes from the linear source (left side of the above image). We can do this because it's a Thevenin simplification, i.e., simplified to a resistor and a voltage.

Then, since we know that $v_o(t)=A_v{v}_i(t)|A_v\in Z$, we can model the input into the load as a Thevenin circuit, with the voltage set as the dependent source $A_v{v}_I$.

This then gets you three parameters:

• $R_{in}$: Input resistance (source, e.g. a battery)
• $R_{out}$: output resistance (load, e.g. an LED)
• $A_v$: voltage gain of the amplifier

Amplifier Types

• Voltage amplifier -> gain is $A_V=\frac{V_o}{V_i}[\frac{V}{V}]$
  • Gain will be very large ($>{10}^5$)
• Current amplifier -> gain is $A_I=\frac{I_o}{I_I}[\frac{A}{A}]$
• Power amplifier -> gain is $A_P=\frac{P_o}{P_i}\left[\frac{W}{W}\right]$
  • Note that a power amplifier is mostly just current amplification usually.

Decibel (dB) Scale

Since the voltage gain in a voltage amplifier is so large, we, by convention, use dB to discuss voltage gain. So:

• Voltage gain in dB expressed as $20{\log }_{10}|A_V|$
• Current gain in dB expressed as $20{\log }_{10}|A_I|$
• Power gain in dB expressed as $10{\log }_{10}|A_P|$
  • This is because:

Chapter 2: Operational Amplifiers

2.1 The Ideal Op Amp

The Operational Amplifier:

• Takes in an inverting input voltage $V_{i+}$, as well as a noninverting input voltage $V_{i-}$
  • $V_{i-}$ is called the noninverting input voltage because it has the same sign as the output, whereas $V_{i+}$ has the opposite sign.
  • In the circuit model of an operational amplifier, $V_{i-}$ is distinguished by a $-$ sign in the triangle symbol, and $V_{i+}$ is distinguished by a $+$ sign.
• Outputs an output voltage that follows this equation (i.e., it scales the difference between the input voltages linearly):

• Has two DC power terminals ($V_{cc},-V_{cc}$) added because it contains semiconductors
  • Output voltage cannot be scaled more than $V_{cc}$.
• Rejects common signals
  • e.g. if $V_{i+}=V_{i-}$, then ideally $V_o=0$.
  • This is known as common-mode rejection

The output voltage $V_o$ can be graphed as follows. Note $|V_o|$ never actually reaches $V_{cc}$, since there is some loss that occurs.

The ideal operational amplifier has:

• Zero input current, i.e. doesn't "bleed" any current to amplify voltage
• Zero output resistance, i.e. zero load voltage
• Infinite op-amp gain: $A_o\to \mathrm{\infty }$
  • This implies that your $V_o$ slope will basically go straight up.

Circuit Model of the Ideal Operational Amplifier

As with the linear amplifier from [[#1.5 Circuit Models for Amplifiers]], we can model the operational amplifier as a circuit - the main difference being that there are two input voltages modelled around the input resistor instead of one.

2.2 The Inverting Configuration

2.3 The Noninverting Configuration

2.4 Difference Amplifiers