1. Circuit I/V models
Many times it is not necessary to solve for the exact diode voltage and current with the Shockley equation. Instead, a simpler model provides adequate and much quicker results. The constant-voltage model provides a good balance between accuracy and analysis ease — it is our most frequently used model. Its behavior can be classified into two states:
- Forward bias (ON)
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\(v_D = v_D(on) \approx 0.6\,\mathrm{V}\). This value depends on the general magnitude of forward currents expected and the diode type (silicon 400-800 mV, germanium 200-400 mV, Schottky 100-500mV, etc.).
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Check: \(i_D \stackrel{?}{\ge} 0\). Positive is good. If zero, you may need to use a better model.
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- Reverse bias (OFF)
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\(i_D = 0\)
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Check: \(v_D \stackrel{?}{\le} v_D(on)\). Usually negative or zero. If in range \(\left[0 \ldots v_D(on)\right]\), you may need to use a better model since this is the range of worst error for this simple model.
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Analyzing a circuit with diodes is then an iterative process of finding the ON/OFF states of the diodes at each time and replacing with the appropriate model. This process becomes quick with practice and helps to understand the overall operation of a circuit.
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Guess the state of each diode
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Analyze the circuit for the diode currents and voltages using the selected models
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Check the values against the model validity V / I conditions
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Repeat until all checks pass simultaneously
2. Simulator model
Figure 2 shows the usual model that a circuit simulator uses for finding the current through a diode. It includes the effects of junction and diffusion capacitances, bulk series resistance, and temperature (including IS's dependence).
This model is “ok” for hand-solving a one-diode circuit, and
no problem for a SPICE simulation, but
a total nightmare for hand-solving a circuit with two or more diodes!
An engineer would choose to analyze a circuit by hand in order to:
understand a circuit’s operation
to develop intuition and so be able to
predict its general behavior under various inputs and other conditions.
SPICE gives numbers not intuition
3. Ideal diode
The simplest possible description of a diode’s behavior is:
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When current flow is positive, the diode behaves like a short-circuit.
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When the voltage is negative, the current is zero.
This is a one-way valve for current.
| “on” state |
vD = 0 and iD > 0 … a short-circuit |
| “off” state |
vD ≤ 0 and iD > 0 … an open-circuit |
The bold inequalities indicate which values of diode current or voltage are set by the rest of the circuit. This is the same way that you can’t know a voltage source’s current by looking at only the source — it depends on what it’s connected to.
A circuit symbol for this is a single-pole single-throw (SPST) switch whose state depends on the local conditions.
(draw this for the ON and OFF states)
The important observation is that these two models are each individually linear. HOWTO use this model when analyzing a circuit with diodes:
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Guess a state for the diode: on/off
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Replace the diode symbol with either a short- or open-circuit. Keep the A/K terminals and don’t collapse the wire so that you can still find the current through the device model.
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Solve the circuit using normal linear circuit analysis tools.
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Check that vD or iD are consistent with your guess.
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If not, then switch the guess to the other state and re-analyze.
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4. Constant voltage model
Go back and look at Figure 1 again.
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The black curve represents the actual I/V curve for a diode.
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The red curve is the I/V curve for the ideal one-way valve or switch model.
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The blue curve is a better match to the actual I/V curve.
The blue model is the constant voltage model and simply adds a voltage source in series with the one-way valve switch.
One important thing to remember is that the internal voltage source must always absorb power. This is easy to ensure by making sure that the diode current is always positive, which is true when the device is forward-biased.