# Independent and Dependent Voltage Source Problems in Simulations

June 20, 2019 Even when I was confident with understanding voltage and current, in my earlier years, I would still run into instances where my power supply simply wasn’t working as intended or working properly. If you are learning more about independent and dependent voltage, allow me to share some of my learning moments so you might have less fumbling to do.

There is an unwritten rule in circuit analysis about voltage and current sources, and it does not become obvious until you start working with real voltage/current sources. When I first started experimenting with power supplies in classes, I soon realized that power supplies do not always supply a fixed voltage and current.

Even circuit simulations still follow the unwritten rule that output from a source never changes. Since this is the case, what is the best way to address independent and dependent voltage source problems in a circuit simulation?

## Independent vs. Dependent Voltage Sources

An independent voltage source (sometimes called an ideal voltage source), always outputs a constant voltage, regardless of what happens elsewhere in the circuit. The same idea applies to an independent current source, where the current output is always the same value regardless of the voltage drop elsewhere in the circuit.

All voltage sources are non-ideal voltage sources. They do not actually output the rated voltage, and the value they output will depend on the load connected to the source.

### An Example: A Battery and a Resistor

Consider a battery as an example. A battery is intended to output a constant voltage based on the electrochemical potential difference between the chemical cells in each terminal. The terminals are conductors, but they have some resistance, thus they drop some voltage. If you connect a battery to a load with resistance that is much higher than the terminal resistance, then the total current in the circuit will be quite small. The voltage dropped across the terminals will also be very small, thus the voltage seen by the load resistor will be very close to the voltage value listed on the battery. In this case, the voltage that actually reaches the circuit remains nearly unchanged, and the battery behaves almost like an independent voltage source.

Now let’s think about what happens in this battery/resistor circuit when the connected resistor is similar to or less than the value of the terminal resistance. In this case, a significant voltage will be dropped across the terminals. If you were to measure the voltage across the load resistor with a multimeter, the voltage that is actually seen by the load resistor is much less than the value listed on the battery.

Why does this happen? What makes the voltage that actually reaches the circuit change? In the case of the battery, this occurs because of the difference in the load and terminal resistance values. Batteries have another limitation in that they can only discharge at a certain rate. According to Ohm’s law, if you connect a conductor with near zero resistance across two terminals of a power source, then the output current should approach infinity. This does not happen in reality. Laboratory power supply

All batteries have a maximum discharge rate, meaning the output current cannot exceed a certain value, even if the battery is shorted with a conductor. In a battery, this depends on the electrochemical reaction used to supply power, the geometry of the cell, and other factors. This limitation on the output current and the voltage that reaches a circuit isn’t limited to batteries; this same limitation applies to any power source and should illustrate why real power sources are actually non-ideal sources.

## Modeling Independent and Dependent Voltage Source Problems

The output from any dependent voltage source depends on the electrical behavior at some other location in the circuit. If you examine the way some simple voltage sources behave, you’ll quickly find that the voltage sources only appear to be independent in certain conditions. When modeling the behavior of a power supply or active component designs using a SPICE simulator, such as an unregulated power supply, switching regulator, or amplifier circuits, you’ll quickly find that the output from the circuit is dependent on the input voltage in some way, thus it is called dependent voltage source.

Modeling the output from the dependent source requires using an independent source as an input. If you want to produce the most accurate results, then this independent source should be modeled as a non-ideal source with a specified terminal resistor. There are two different circuit models for modeling non-ideal sources.

The Thevenin model is used for an independent voltage source, and the Norton model is used to an independent current source. The terminal resistor in a Thevenin circuit is placed in series and is very small (usually a few Ohms), and the terminal resistor in a Norton circuit is placed in parallel and is very large (usually MOhm levels).

The goal with modeling a design for a dependent current source is to create a graph showing the output voltage vs. the input voltage. For purely linear dependent voltage sources, the output should be a linear function of the input voltage. You can sweep through different input voltages from the independent source and model the output from the dependent source using typical circuit analysis techniques. You can then determine the right function that describes the output voltage from the dependent source in terms of the input voltage. A dual DC power supply is one example of a dependent voltage source

Note that the above discussion applies to DC voltage sources. When working with AC voltage sources, you need to consider the impedance of the output. Ideally, the output impedance spectrum will be flat over a large range of frequencies, and this is normally the case for adjustable AC power supplies.

In a circuit model for independent and dependent voltage source problems, you could specify different output impedance values for the independent source. When designing an independent AC source, you will want to examine how the function defining the output voltage changes as a function of frequency. For a good dependent AC power source, the output voltage function should exhibit very small changes with frequency.

Circuit analysis is much easier when you work with a complete circuit simulation package. The OrCAD PSpice Simulator from Cadence allows you to build circuit models for your design and analyze their behavior using a graphical interface. This unique package is specifically adapted to complex PCB designs.

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