Circuits and Electronics MITx 6.002 Notes

Last Updated: September 09, 2021 by Pepe Sandoval

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- Circuit Sandbox Simulator Usage
- Drag and drop components from right components panel (Copy and paste components is possible and use R to rotate). E.x. Drag and drop DC source and resistors
- Double click components to edit properties. E.x. Double click source to edit voltage and resistance (3k)
- Add probes (if needed).
- For DC analysis you can add current measurement probes
- For Transient analysis you can add Voltage and current probes (simnulate osciloscope probes)

- Connect components by click and drag between connection points

- Types of Analysis / Simulation tools
**Direct Current (DC Analysis)**Determines voltages and currents in your circuit at time $t=0$, values are relative to GND (reference node)**Transient Analysis (TRAN Analysis)**determines Voltage and current in your circuit over a specified time interval $t_0<t<t_1$- As input usally needs an end time or time interval

**Alternate Current (AC Analysis)**Lets us figure out how our circuit behaves with different frequency signals (Between $f_0<f<f_1$). AC Analysis calculates our circuit frequency response, we can see voltage or current signal behavior over a whole range of frequencies without having to do a bunch of individual transient analysis and then plotting the resulting graphs ourselves.- Plots shows the magnituve (dB) and phase (Radians) of the response relative to the input
- As inputs usually needs the frequency interval and source name (It is recommened to name input source
`src`

to use in AC analysis) - Frequency in x-axis is in log scale so $1->10^1=10$,$2->10^2=100$,$1->10^3$=1000

Decibels (dB)expresses the log of ratio of two values (in other words the log of the division of Output divided by Input) $$M_{dB} = 20\log(\dfrac{V_{out}}{V_{in}}) -> V_{out} = V_{in} * 10^(\dfrac{M_{dB}}{20})$

Differential equations of the form $$Ax'(t) + Bx(t) +f(t) ; x = x(t)$$

First order (only one derivative), coefficients of $x$ are constants, $f(t)$ is a known function and we want to find $x(t)$

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