# Dependent Sources

**Dependent Sources** are sources for which the output value *depends* on a **voltage **or **current **in the circuit. Many electronic devices behave this way where the output is dependent on voltages or currents in the circuit.

A *diamond* symbol is used to represent a **dependent source**:

The circuit shown below features a dependent *voltage source* where the voltage supplied depends on the voltage across the series resistor R multiplied by a constant a:

One thing to be careful of with dependent sources is when applying *Superposition*. When using superposition, dependent sources **cannot** **be removed** and must **always** remain in place for each circuit analyzed in turn.

Similarly dependent sources cannot be removed when determining *Thevenin* or *Norton* equivalent circuits.

## Types of dependent sources:

There are **four** types of *dependent sources* as follows:

**(a) Voltage-controlled voltage sources(VCVS)** where the **output voltage** is controlled by a *voltage* in the circuit:

**(b) Voltage-controlled current sources(VCCS)** where the **output current** is controlled by a *voltage* in the circuit:

**(c) Current-controlled voltage sources(CCVS)** where the **output voltage** is controlled by a *current* in the circuit:

**(d) Current-controlled current sources(CCCS)** where the **output current** is controlled by a *current* in the circuit:

### Examples:

**1.** Determine the output voltage of the VCVS source in the circuit below:

**2.** Determine the output current of the VCCS in the circuit below:

**3.** Determine the output voltage of the CCVS in the circuit below:

**Node Va:**Note that in the above we have a single equation with two unknowns so we need another equation to determine Va and Vb to find I3. We can apply KCL at node Vb: We can then solve for Va and substitute this back into [1] to determine

**Vb**:

**4.** Determine the output current of the VCCS in the circuit below:

**KCL**at

**node a**and solve for

**voltage a**: Hence the output current is -202mA, i.e. the current is flowing

**downwards**(opposite direction to our arrow assignment).

### Questions:

** 1. **Determine the output voltage of the VCVS source in the circuit below:

#### Answer

** 2. **Determine the output current of the VCCS source in the circuit below:

#### Answer

## Lab:

Is there a way to model dependent sources in LTSpice? Good news, the answer is yes! So let's see how that works.

Let's consider a simple circuit which uses a VCVS such as the one below:

How can we model this in LTSpice? Let's begin by placing down the components we know from past experience:

So far so good, but how do we now places that VCVS? One answer is by taking a look through the component viewer and stumbling upon this component:

Whoa, what just happened? What are we looking at here? Well it turns out we get a 4 terminal device where the two terminals at the top are to be connected to the **voltage **we **depend on **which in this case is effectively the** voltage across R1.**

We then need to specify the "Value" field which denotes the gain of the dependent source which let's say is 2, i.e. a=2.

We can then measure the voltage across the dependent source to be 10V.