555 Timer Integrated Oscilloscope

One Shot Pulse (555 Timer) Simulator

Circuit Parameters

C1 (µF)

R1 (Ω)

Pulse Width (ms)

Capacitor Voltage vs Time

                        Calculated Pulse Width: 0.000 ms
                    

Recommended Components

Recommended capacitor for C1 will appear here after calculation.

Quick Math
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Dimensional Analysis:

How do we get time from farads and ohms?

We want to show that:
[Resistance] × [Capacitance] = [Time]

Start by expanding the units:
[Ω] = V/A
[F] = C/V
[C] = A⋅s

Now put it together:
(V/A) ⋅ (C/V) = C/A = (A⋅s)/A = s

This proves that multiplying resistance (ohms) by capacitance (farads) 
gives us time (seconds), which is why RC has units of time!

Capacitor Charging: V(t) = Vcc × (1 − e^−t/RC)

Charging Equation Derivation

1. Start with Kirchhoff's Voltage Law:
   Vcc = VR + VC
   where VR is voltage across resistor and VC is voltage across capacitor

2. Ohm's Law for resistor:
   VR = i × R
   where i is current through the circuit

3. Capacitor current-voltage relationship:
   i = C × dVC/dt

4. Substitute into KVL:
   Vcc = (C × dVC/dt × R) + VC

5. Rearrange differential equation:
   dVC/dt = (Vcc - VC)/(RC)

6. Solve using separation of variables:
   ∫dVC/(Vcc - VC) = ∫dt/(RC)
   -ln(Vcc - VC) = t/(RC) + K
   where K is integration constant

7. Solve for VC:
   Vcc - VC = e^(-t/RC - K)
   VC = Vcc - e^(-t/RC - K)

8. Apply initial condition VC(0) = 0:
   0 = Vcc - e^(-K)
   e^(-K) = Vcc

9. Final charging equation:
   VC(t) = Vcc × (1 - e^(-t/RC))

Capacitor Discharging: V(t) = Vcc × e^−t/RC

Discharging Equation Derivation

1. Start with Kirchhoff's Voltage Law:
   VR + VC = 0
   where VR is voltage across resistor and VC is voltage across capacitor

2. Ohm's Law for resistor:
   VR = i × R
   where i is current through the circuit

3. Capacitor current-voltage relationship:
   i = -C × dVC/dt
   (negative sign because current is leaving capacitor)

4. Substitute into KVL:
   (C × dVC/dt × R) + VC = 0

5. Rearrange differential equation:
   dVC/dt = -VC/(RC)

6. Solve using separation of variables:
   ∫dVC/VC = -∫dt/(RC)
   ln(VC) = -t/(RC) + K
   where K is integration constant

7. Solve for VC:
   VC = e^(-t/RC + K)

8. Apply initial condition VC(0) = Vcc:
   Vcc = e^K

9. Final discharging equation:
   VC(t) = Vcc × e^(-t/RC)

Monostable Mode: 2/3 Vcc = Vcc × (1 − e^−t/RC)
2/3 = 1 − e^−t/RC
e^−t/RC = 1/3
−t/RC = ln(1/3)
t = RC × ln(3) ≈ RC × 1.0986

Monostable Timing Derivation

1. Start with charging equation:
   V(t) = Vcc × (1 - e^(-t/RC))

2. Set V(t) = (2/3)Vcc:
   (2/3)Vcc = Vcc × (1 - e^(-t/RC))

3. Divide both sides by Vcc:
    2/3 = 1 - e^(-t/RC)

4. Solve for exponential:
    e^(-t/RC) = 1 - 2/3 = 1/3

5. Take natural logarithm:
    -t/RC = ln(1/3)

6. Solve for t:
    t = -RC × ln(1/3)
    t = RC × ln(3)
    t ≈ RC × 1.0986

Note: This is the time it takes for the capacitor to charge from 0V to 2/3 Vcc,
which triggers the 555 timer's internal comparator.

Why did I do this?

This 555 timer simulator was created as part of my ECE 227 Lab course project. I needed to design a clock pulse generator for a binary counter that would cycle through an 8-to-1 multiplexer. The 555 timer IC was the perfect solution for generating precise clock pulses, and this simulator helped me understand and visualize how the timing components (resistors and capacitors) affect the output frequency. The charging and discharging formulas used in this project directly relate to the RC circuit concepts I learned in my Physics II class, making this a great way to bridge theory with practical application.

One Shot Pulse (555 Timer) Simulator

Circuit Parameters

Recommended Components

555 Timer Pinout and Internal Schematic

Why did I do this?

How to Use the 555 Timer Simulator

Understanding the Voltage vs Time Curve