# An In-Depth Dive Into Series vs. Parallel Circuits

### Key Takeaways

• Learn the basics of elements in series and parallel

• Parallel and series circuits utilizing transistors

• A discussion of series vs. parallel resonant circuits

A figure illustrating a parallel circuit on the left and a series circuit on the right

Ultimately, the difference between a series and parallel circuit can be summarized in the following two sentences.

In a series circuit, components are connected from end to end, creating a single path for current to flow. All elements within the circuit have the same current running through them.

In a parallel circuit, all components are connected, sharing two electrical nodes. Each component has the same voltage across it.

Of course, most circuits nowadays are neither purely series nor purely parallel, but a mix of both. Oftentimes, you will see subcircuits within a larger circuit that contain parallel elements or series elements.

We’ll be providing basic examples with resistors as an arbitrary two-terminal device, but these definitions are also applicable to capacitors and inductors. We’ll then be discussing more complex series vs. parallel circuits with transistors, inductors, and capacitors.

## Elements in Series

Schematic with resistors R1 through R4 in series

The term series circuit refers to the components connected end-to-end, as illustrated in the figure above. For example, the voltage source supplies a voltage and causes current to flow in the single branch in the circuit, through R4 all the way to R1.

In order to calculate the voltage drop across each resistor, you can use Ohm’s law and multiply the current in the branch (the same current through each resistor) by its resistance. Another method of calculating the voltage drop across each resistor is treating it as a voltage divider and using the corresponding voltage divider equation.

## Elements in Parallel

Schematic showing R1 through R3 in parallel

In a parallel circuit, all components have two common electrical nodes. In most circuits, wires are assumed to have zero voltage drop across them, and as such, all nodes that are connected by wires have the same voltage at that point. As shown in the image above, resistors R1, R2, and R3 all have an electrically common node at the bottom (which happens to be connected to the negative terminal of the battery), and an electrically common mode at the top (which happens to be connected to the positive terminal of the battery).

As all components share two common electrical nodes, they all have the same voltage drop. In the image, the nodes are electrically connected to the positive and negative terminals of the battery, and as such, all resistors have a voltage drop proportional to V.

## Parallel Circuits With BJT Transistors

Transistors in parallel can be used to help regulate current in the case that an individual transistor may not be sufficient. With multiple transistors in parallel, the current handling capacity can be better handled and prevents any individual transistor from sustaining damage.

For example, suppose we wanted to power a motor that required current (1.5A) larger than a single transistor (1A)  could provide. Adding a second transistor would allow for a total safe current draw of up to 2A–enough to power the motor. If the motor was connected to the supply, then the collector of both BJTs could be connected to the second terminal, with all three sharing a common node. The base of both transistors would be connected to the motor control and the emitters to ground.

This can be useful if both transistors (and any other passive components used) are perfectly matched. In reality, this is rarely the case, and thermal runaway or mismatch can occur. This happens when there is a mismatch in the fabrication between transistors, leading a single transistor to draw more current than the other, which can cause permanent damage.

For this reason, you should utilize a low-valued resistor in series with every emitter. This provides negative feedback; as in the case of overcurrent, the node at the emitter of the BJT will increase, resulting in a smaller VBE and thus less current draw.

## Parallel and Series Circuits With MOSFET Transistors

An especially common application is in CMOS (complementary metal oxide semiconductor) logic. Picture a NAND gate; transistors below the node labeled “out” are NMOS transistors while transistors above the node labeled “out” are PMOS transistors.

The NMOS transistors are in series. If both A and B are high, then both transistors conduct current. The same current that enters the top NMOS (input A) at the drain exits the bottom NMOS (input B). For transistors in series, both must present a low resistance connecting the output to the supply voltage, essentially creating an AND gate.

The two PMOS transistors are in parallel, and both nodes of the PMOS transistors are connected to Vdd and to “out,” meaning that when not-conducting, there is the same voltage drop across them. When a current path has two transistors in parallel, one or both the transistors must present low resistance connecting the supply voltage with the output, creating an OR gate.

## Resonant Series vs. Parallel Circuits

Another common use of parallel and series circuits is creating an LC resonant tank. An LC circuit, also known as a tank circuit or tuned circuit, consists of an inductor (L) and capacitor (C), connected either in parallel or in series. They are especially useful for generating signals at given frequencies or filtering out specific frequencies from a more complex filter.

When oscillating at its natural resonant frequency, an LC circuit will have the capacitor store energy in the electric field and the inductor store energy in the magnetic field. They can be used for a variety of applications including tuning transmitters, induction heating, and building filters.

In some cases, you’ll be able to convert series resonant circuits to parallel and vice versa, depending on the frequency of interest. Using a series-to-parallel converter online may help.

### Series LC Tank

In series configuration, the capacitor and inductor are connected in series. The total voltage across the circuit block is the superposition of the voltage across both the capacitor and inductor, and they all share the same current. As frequency increases, the inductor presents more reactance and the capacitor presents less. At a given frequency, the reactance of the inductor and capacitor are equal, which is the resonant frequency.

At resonance, the reactances cancel each other out and the current is maximized. The equivalent circuit impedance is minimal–this is why series LC circuits are called acceptor circuits. When connected in series with a load at resonance frequency, the circuit will act as a band-pass filter with zero impedance. A series resonant circuit can provide voltage magnification.

### Parallel Resonant Circuit

In parallel LC circuits, the voltage across the circuit block is equal to the voltage across the inductor, which is the same as the capacitor. The current flowing through the block is equal to the sum of the current through the inductor and capacitor.

At resonance, the reactance of the capacitor equals that of the inductor and they cancel each other out. In theory, there would be zero current drawn from the terminals, with current circulating simply between the inductor and capacitor.

At resonant frequency, the impedance of the resonant parallel circuit reaches infinity. Therefore, connecting the circuit in series with a load will act as a band-stop filter, while connecting the load in parallel will act as a band-pass filter.

Parallel resonant circuits can provide current magnification and can also be used as a load impedance in the outputs of RF amplifiers. Because they present a high impedance at the frequency of interest, the gain of the amplifier can reach maximum.

When considering series vs. parallel circuits in your design, make sure to optimize Cadence’s suite of design and analysis software. You’ll be able to get access to a complete set of schematic capture tools, simulation capabilities, and other powerful CAD features.

In case you are seeking to use either resonant series or parallel circuits in your RF designs, make sure to check out RF Design: The Wave of the Future for more information.

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