#31 Operational Amplifiers #31 — Op-Amp basics

Below are all the lines written in the notebook together with the full narration transcript.

1. 1. What is an op amp?

   

   What is an op amp?

   Operational amplifier

   Many internal parts, one external block

   Comparison and voltage following

   Inverting / non-inverting gain

   Summing, differentiation, integration

   An amplifier that performs signal operations

   Narration transcript

   In this lesson, the goal is not to solve a long numerical problem yet. The goal is to meet the operational amplifier, or op amp, and understand what kind of circuit element it represents. An op amp is built from many transistors, resistors, capacitors, and diodes, but in circuit theory we usually treat it as one block. That block can be used for comparison, voltage following, inverting amplification, non-inverting amplification, summing, differentiation, integration, and many other operations. So the name operational amplifier is literal: it is an amplifier used to perform operations on signals.

2. 2. Symbol and pins

   

   Symbol and essential pins

   741: a common op-amp example

   Pin 2: inverting input (−)

   Pin 3: non-inverting input (+)

   Pin 6: output v_o

   Pin 7: +V_CC; pin 4: −V_CC

   Supply pins are required even if omitted

   Narration transcript

   Now let us connect the physical part to the schematic symbol. A common op amp such as the seven forty one has several package pins. For circuit analysis, the most important pins are the inverting input, the non-inverting input, the output, and the two supply pins. The inverting input is marked with a minus sign. The non-inverting input is marked with a plus sign. The output is drawn at the tip of the triangle. The supply pins, V plus and V minus, power the device, even when they are not always drawn in every small signal schematic.

3. 3. Ideal model

   

   Ideal op-amp model

   $v_{\mathrm{o}}=A(v_{+}-v_{-})$

   A→∞

   R_in→∞

   $i_{+}=i_{-}=0$

   R_out→0

   These are ideal analysis assumptions

   Narration transcript

   For the first pass, we use the ideal op amp model. There are three assumptions to keep in mind. First, the open loop gain is extremely large, so ideally A goes to infinity. Second, the input resistance is extremely large, so no current enters either input terminal. We write i plus equals zero and i minus equals zero. Third, the output resistance is approximately zero, so the op amp behaves like a strong voltage source at its output. The basic controlled-source idea is v output equals A times v plus minus v minus.

4. 4. Output limits

   

   Output limits

   An op amp does not create energy

   $-V_{\mathrm{CC}}\le v_{\mathrm{o}}\le +V_{\mathrm{CC}}$

   Demand beyond a rail causes saturation

   The waveform clips

   Real swing may not reach the rails

   Check the device data sheet

   Narration transcript

   The ideal model is a tool, not a real power supply. In a practical op amp, the output voltage cannot become larger than the supply rails. If the op amp is powered from plus V C C and minus V C C, then the output is limited to that range. When the requested output tries to go beyond the rail, the waveform clips. So when we analyze op amp circuits, we first use the ideal rules, but we also remember that the final output must stay inside the available supply range.

5. 5. Input signs

   

   Input signs

   v₊↑ → v_o↑

   v₋↑ → v_o↓

   $v_{\mathrm{d}}=v_{+}-v_{-}$

   v_o=Av_d

   Open-loop operation is very sensitive

   The signs set the feedback direction

   Narration transcript

   The plus and minus signs tell us the direction of the effect. If the non-inverting input, v plus, becomes larger, the output tends to rise. If the inverting input, v minus, becomes larger, the output tends to fall. That is why the upper input is called inverting: a positive change there pushes the output in the opposite direction. This sign convention is the key to understanding why feedback can force the two input voltages to become almost equal in many linear op amp circuits.

6. 6. First inverting circuit

   

   First circuit — inverting form

   V_i → R₁ → minus input

   Plus input → ground

   Output: V_o

   R_f: V_o back to the minus input

   This path is negative feedback

   Goal: controlled linear gain

   Narration transcript

   Here is the first circuit we will recognize: the basic inverting op amp. Read it slowly from left to right. The input voltage V i passes through resistor R one and reaches the minus input node. The plus input is connected to ground. The output is V o on the right. A feedback resistor R f connects the output back to the same minus input node. This feedback path is not decoration. It is the path that makes the circuit operate as a controlled amplifier instead of as an open loop comparator.

7. 7. Feedback path

   

   Input and feedback paths

   Input: V_i → R₁ → v₋

   Feedback: V_o → R_f → v₋

   $i_{-}\approx 0$

   $v_{+}=0 V$

   Negative feedback + linear region: v₋≈v₊

   v₋≈0 V: conditional virtual ground

   Narration transcript

   Let us mark the important parts. The red path is the input path through R one into the minus input node. The orange path is the feedback path through R f from the output back to that same node. Because the ideal op amp input current is zero, almost no current enters the minus terminal. Since the plus terminal is grounded, v plus is zero. In the next lesson, negative feedback will let us treat the minus node as almost zero volts as well. That idea is called virtual ground, and it leads to the inverting amplifier gain formula.

8. 8. Method summary

   

   Method summary

   Plus input, minus input, and output

   A→∞, R_in→∞, R_out→0

   $i_{+}=i_{-}=0$

   Output is limited by the supply rails

   R_f supplies feedback in the inverting form

   Next: inverting-amplifier gain

   Narration transcript

   So the handoff from this introduction is simple. An op amp has a plus input, a minus input, an output, and supply limits. In the ideal model, the input currents are zero, the input resistance is infinite, the output resistance is zero, and the gain is very large. The first circuit to recognize is the inverting op amp: V i goes through R one to the minus input, the plus input is grounded, and R f feeds the output back to the minus input. Next, we will calculate exactly how that circuit amplifies and inverts the input signal.

Source video: Circuit Theory #31 | Operational Amplifiers - Op-Amp Basics (5:13)