Circuits and Electronics 1: Basic Circuit Analysis

Circuit Simulator

• Circuit Sandbox Simulator Usage
  1. 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
  2. Double click components to edit properties. E.x. Double click source to edit voltage and resistance (3k)
  3. 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)
  4. 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})$

Linear First Order Constant Coefficient Differential Equations

• 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 $x(t)$

References

• Circuits and Electronics 1: Basic Circuit Analysis edX Course
• Circuit Sandbox Simulator (Spinning Numbers Circuit Simulator)
• Spinning Numbers: Circuit sandbox Docs
• Spinning Numbers Website