# 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:

The output voltage of the VCVS is equal to 2V1 so the first step is to determine V1. Looking at the circuit fragment on the left we see VS in series with R1 which means that VS is dropped across R1, i.e. V1=Vs=5V. With V1 now known the dependent voltage outputs 2x5 = 10V

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

The output current of the VCCS is equal to 4V2 hence the first step is to determine V2: Considering the circuit fragment on the left hand side we have a voltage source driving a voltage divider circuit, so the voltage divider rule can be used to calculate V2: The VCCS is then outputting 20A.

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

We can apply nodal analysis to solve this more complex circuit, to assist with this let's go and redraw the circuit highlighting the nodal voltages: Applying KCL at 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  to determine Vb:

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

As above we can apply nodal analysis to determine the voltage at node a and then solve for the output of VCCS. First step is to label the node and currents From here we can apply 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:

5V

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

12.5A

## 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.