Resistor inductor circuit
An RL circuit, also known as a resistor-inductor circuit or RL network, comprises a combination of inductors and resistors and is commonly energized by a power source. It involves connecting an inductor and a resistor in either a parallel or series configuration. These circuits can be driven by either a current source (in parallel) or a voltage source (in series). Alongside capacitors (C) and resistors (R), inductors (L) constitute the fundamental passive linear circuit elements. Together, they can form electrical circuits in various configurations such as the RC circuit, LC circuit, and RLC circuit.
Alternatively, an RL circuit can be defined as an electrical circuit incorporating resistance and self-inductance. Induction occurs when an electromotive force (emf) source applies a continuous change in magnetic flux. Mutual inductance arises from Faraday’s laws of induction, while self-inductance is an effect of Faraday’s laws of induction on a device acting upon itself. The inductor, a component exhibiting self-inductance, plays a pivotal role in the circuit. However, due to the presence of a resistor in the ideal circuit, an RL circuit will dissipate energy, akin to an RC or RLC circuit.
Types of RL circuit
RL circuit depending on the way the resistor and inductor are connected can be classified in the following ways:
- Series RL circuit
- Parallel RL circuit
Series RL circuit forming low pass filter
A series RL circuit is a type of electrical circuit that contains a resistor (R) and an inductor (L) connected in series to a voltage source as shown in Fig 1 and 2. In this configuration, the current through all the components (R, L, and voltage source) is the same. The series RL circuit is powered by a voltage source (such as a battery or an AC power supply) that provides the electrical potential necessary for the circuit to operate.
If the output is taken across the resistor (as shown in Fig 1), the circuit’s transfer function is a low-pass filter.
Frequency response
The transfer function of above RL circuit is :
$$\cfrac{v_{out}(\omega{})}{v_{in}(\omega{})}=\cfrac{R}{R+j\omega{}L}$$
Comparing it with low-pass transfer funciton:
$$\cfrac{v_{out}(\omega{})}{v_{in}(\omega{})}=\cfrac{A}{1+j\omega{}/\omega{}_c}$$
We obtain,
$$A=1$$
$$\omega{}_c=\cfrac{R}{L}$$
ωc is the -3dB point of the transfer function. It is also called the cutoff frequency. It is the frequency where the transfer function’s gain falls by 3dB. At this frequency, the phase drops by 45°.
Step response
Steady-state sinusoid response
Series RL circuit forming high pass filter
If the output is taken across the inductor (as shown in Fig 2), the circuit’s transfer function is a high-pass filter.
Frequency response
Steady-state sinusoid response
Step response
Parallel RL circuit
Frequency response
Step response
Steady-state sinusoid response
