A voltage source, which falls under the category of an active element, supplies a defined and constant voltage across its terminals. This voltage doesnt change in response to any other components in the circuit. But practically, or real-world voltage sources deviate from this ideal behavior. The rated voltage across the terminals decreases as the load current they supply increases.
You have come across two basic elements in electrical or electronics circuits throughout all of the tutorials you have completed thus far: active elements and passive elements. Batteries, generators, and operational amplifiers are examples of active elements that can continuously supply energy to a circuit. On the other hand, passive components, such as resistors, capacitors, and inductors, are made of physical materials and are incapable of producing electricity on their own. Their only function is to use up the energy that is supplied to the circuit.
Active Elements: Power Suppliers. The active elements that continuously supply electrical energy to the connected circuits or networks are among the most critical elements in the world of electrical circuits. Fittingly, these elements are called “electrical sources.” Electrical sources can be divided into two categories: voltage sources and current sources.
Voltage Source vs. Current Source: In circuits, current sources are typically less prevalent than voltage sources. Still, each type has a place and can be seen as a complement to the other.
Electrical sources: Powering the circuit. An electrical supply, commonly referred to as “a source,” is a tool used to introduce electricity into a circuit. There are two primary types of these sources: voltage sources and current sources. Direct current (DC) and alternating current (AC) sources can be applied to both kinds of sources. An AC source produces a voltage that varies sinusoidally with time, whereas a DC source produces a voltage that is constant.
Examples: Differences Between DC and AC Sources: A common illustration of a DC source is a battery. On the other hand, an example of an AC source is the 220V wall socket or mains outlet in your house.
Energy Conversion: A Hidden Ability of Electrical Sources: We already know that circuits receive energy from electrical sources. An amazing bonus, though, is that they can also transform non-electrical energy into electrical energy and the other way around! A battery, for example, converts chemical energy into electrical energy. On the other hand, mechanical energy is converted into electrical energy by an electrical device such as a DC generator or an AC alternator.
Renewable Energy Sources: Energy from sunlight, wind, and tides may be converted into heat or electricity using renewable technology like solar panels and wind turbines. However, they are capable of more than only conversion. These sources provide a two-way flow of energy by serving as both energy providers and absorbers.
I-V Characteristics: An electrical source’s I-V (current-voltage) characteristic curve is another essential feature that determines how it operates. As seen in the figures, this curve offers a useful visual depiction of the source, illustrating its behavior as a voltage source or a current source.
I-V Characteristics of Electrical Sources
Types of Electrical Sources: Dependent vs Independent
Electrical sources can be classified as independent (ideal) or dependent (controlled), regardless of whether they are voltage or current sources. Dependent sources are those whose value is contingent upon a voltage or current in another part of the circuit. This regulating current or voltage may change over time or remain constant.
Ideal vs. Real Sources in Circuit Analysis
Electrical sources are frequently regarded as “ideal” while doing circuit analysis utilizing circuit laws. In theory, this perfect source is able to provide an endless supply of energy with no losses. On a graph, its behavior is depicted as a straight line. However, real-world or practical sources are not ideal. There is usually some resistance associated with them. This resistance may affect the output of a source by connecting itself in series or parallel to a voltage or current source.
The Voltage Source
A voltage source functions as a conductor to allow current to flow through a circuit, such as a battery or generator. It accomplishes this by determining the potential difference, or voltage, between two particular locations.
Consider this voltage to be the equivalent of a pressure differential, like forcing water through a pipe. Just as pressure differences cause water to flow, voltage differences force current to flow across the circuit.
One important thing to keep in mind is that voltage may exist independently of current flow, just like water pressure can in a closed pipe. The battery is the most used voltage source in circuits.
Similar to a water pump’s pressure gauge, the voltage you measure across a battery’s positive and negative terminals is referred to as the terminal voltage.
The Ideal Voltage Source:
A two-terminal active element with the capability of continuously supplying and maintaining the same voltage (v) across its terminals regardless of the amount of current (i) flowing through it is the ideal voltage source. Put more simply, it produces a constant voltage independent of the current it supplies. Its I-V characteristic curve shows a straight line as a result of its flawless behavior.
The Nature of the Ideal Voltage Source Is Independent and Constant
The name “Independent Voltage Source” is another name for this ideal voltage source as it is not dependent on any of the following two factors:
- The amount of current passing through the source, regardless of the amount of current it is pushing.
- The current’s direction (it can flow in any way)
The voltage of the source is only governed by its internal characteristics. Consider an automobile battery, for instance. Its 12V terminal voltage is fixed as long as there is not a high current drain from it. This battery demonstrates its two-way flow capabilities by being able to give electricity to the automobile in one direction and consume power (charging) in the other.
Dependent Voltage Source: Not Functioning Alone.
A Dependent Voltage Source, often referred to as a Controlled Voltage Source, is not independent like its ideal counterpart. Something else in the circuit must happen before it may output voltage (magnitude). This “something else” can consist of:
- The voltage across an additional circuit element (the amount of voltage present in other places)
- The circuit element through which current is passing (the amount of current flowing elsewhere)
The standard symbol for dependent voltage sources is a diamond. Because they represent various electronic components that are equivalent electrical sources, they are useful tools for simulating the behavior of components like transistors and operational amplifiers.
Connecting Ideal Voltage Sources
Ideal voltage sources can be connected in series or parallel, just like any other circuit element. Recall the characteristics of voltage in parallel and series connections.
Series Connection: The voltages of the ideal sources add up when they are connected in series. When batteries are stacked, the total voltage generated is equal to the sum of the voltages of the individual batteries.
Parallel Connection: All of the optimal voltage sources in a parallel connection have the same voltage level. Imagine that you are joining several water pumps to one pipe; the pressure (voltage) stays the same all the way through the pipe.
Connecting Voltage Sources in Parallel
Parallel Ideal Sources: A Special Case
Parallel connections between ideal voltage sources of the same voltage are typically avoided for circuit analysis. In the shown example diagram, a total voltage of 10 volts is still provided between points A and B by connecting two 10-volt sources in parallel. For simplicity’s sake, though, just one 10-volt supply should be utilized.
No-Nos for Ideal Voltage Source Connections
When connecting ideal voltage sources, keep the following in mind:
- Unequal Voltages: Avoid connecting ideal voltage sources in parallel that have different voltage levels. Unpredictable current behavior and circuit problems may result from this.
- Short Circuits: A short circuit with an external closed loop or branch should not be created by connecting ideal voltage sources in this manner. It would be detrimental to both the source and the circuit to short circuit a battery.
Incorrectly Connected Power Sources
In circuit analysis, while ideal voltage sources with the same voltage are desirable for parallel connections, working with varying levels of voltage makes things more intriguing. These mismatched sources may be analyzed in circuits as long as other circuit elements are available, according to Kirchhoff’s Voltage Law (KVL).
Ideal voltage sources with varying voltages could be connected in series, as opposed to parallel connections. As a result, a single combined voltage source can be created. Depending on how they are connected, the output voltage of this combined source will be equal to the sum (series-aiding) or difference (series-opposing) of the different source voltages. When batteries are linked in series, their voltages might be added (positive terminals connected) or subtracted (opposite terminals connected).
Connecting Voltage Source in Series
Series-Aiding: Boosting Voltage by Connecting Sources
The term “series-aiding” refers to the process of connecting ideal voltage sources in series to increase total voltage. Current can flow through both sources in the same direction in this configuration because the positive terminal of one source is connected to the negative terminal of the other.
Imagine it like connecting the positive and negative ends of batteries. The voltages of the two sources (10V and 5V) in the above example just add up. As a result, terminals A and B are connected to a combined voltage source (VS) of 15V (10V + 5V). It is similar to combining the power of two batteries!
Series-Opposing: A Voltage Tug-of-War
An alternative method of connecting ideal voltage sources in series is called series-opposing. The positive and negative terminals are tied in this instance because the polarities have been reversed. This results in a form of voltage tug-of-war. Consider joining positive to positive or negative to negative battery connections.
The voltages of the 5V and 10V sources are removed in the second circuit example. A combined voltage source (VS) of 5V across terminals A and B is the result of subtracting the lower voltage (5V) from the larger voltage (10V). It functions similarly to one battery partially offsetting the voltage of the other.
The “winner” of the voltage tug-of-war determines the polarity of terminals A and B in series-opposing connections. In the example, polarity is determined by the bigger voltage source (10V), which makes A positive and B negative. This results in a net voltage of +5 volts across them.
It’s a draw if the voltages in series opposition are equal! One voltage totally cancels out the other, resulting in zero voltage between A and B. Since current cannot flow without voltage, just as water cannot flow without pressure, this 0 voltage also indicates that there is no current flow (I).
Solving a Problem of Series-Aiding Sources
Lets analyze a circuit with two series-aiding ideal voltage sources (5V and 12V) supplying a load resistor of 90 ohms. We need to find:
- Source voltage (VS): This is the combined voltage of the two sources in series.
- Load current (IR): This is the current flowing through the resistor.
- Power dissipated (P): This is the power wasted as heat by the resistor.
We’ll also need a circuit diagram to visualize the connections.
- VS = V1 + V2
- = 5 + 12
- = 17 V
- IR = VS / R
- = 17 / 90 Ω
- = 188 mA
- PR = I2R
- = 0.1882 * 90
- = 3.18 watts
Therefore, VS = 17V, IR = 188 mA or 0.188 A, and PR = 3.18 W.
Real World or Practical Voltage Sources
Remember ideal voltage sources? They supply a constant voltage independent of current flow, making them ideal for paper-based circuit analysis. However, things become a little trickier in real life. In contrast to ideal voltage sources, practical voltage sources exhibit a decrease in terminal voltage with an increase in load current.
What makes a difference? Ideal voltage sources function like perfect voltage pumps because they have zero internal resistance (RS = 0). No matter how little, inherent resistance exists in all power sources. With increased load currents, this internal resistance is what lowers the terminal voltage.
Unlike ideal voltage sources, practical voltage sources, such as batteries, come with a hidden enemy, which is its internal resistance (RS). When connected in series with the ideal voltage source, this internal resistance functions just like a standard resistor. Why? Because the circuit’s internal resistance and a series resistor both of them deliver the same amount of current, as depicted in the following diagram.
Comparing Ideal and Practical Voltage Source
Practical voltage sources, such as batteries, exhibit startling similarities to Thevenin’s equivalent circuits.
According to Thevenin’s theorem, every circuit containing resistors and sources (voltage or current) may be reduced to a single voltage source (VS) connected in series with a single resistance. We can simulate practical voltage sources just like this!
The source resistance (RS) holds the secret. The practical voltage source operates almost ideally when RS is quite low. An indefinitely high RS, on the other hand, indicates that the source is effectively “open” (no current flow). So, knowing source resistance allows us to bridge the gap between ideal and real-world voltage sources.
Real Voltage Sources and Dropping Voltage: The I-V Curve Explains the Truth
Real-world voltage sources are flawed by internal resistance (RS), in contrast to ideal voltage sources, which have a perfect voltage output. This RS, no matter how little, influences the source’s I-V characteristic, or the behavior of voltage vs current. This is the reason why:
Internal Resistance Is Important: The voltage measured at the terminals (VOUT) actually decreases as load current increases. This is because, in accordance with Ohm’s Law (V = I * R), the same load current passes through the internal resistance (RS), resulting in a voltage drop.
Real vs. Ideal: Since there is no internal resistance in an ideal voltage source (RS = 0), the ideal source voltage (VS) and the terminal voltage (VOUT) are equal.
The KVL Formula Kirchhoff’s Voltage Law (KVL) clarifies this behavior for us. The terminal voltage can be expressed as the ideal voltage minus the voltage drop across the internal resistance using the equation:
VOUT = VS – i * RS.
Plotting the Impact: The I-V characteristic curve of a real voltage source may be created by plotting this equation. The resulting curve will have a -RS negative slope and be straight. The curve intersects the voltage axis at the ideal voltage source (VS) when there is no current (i = 0). This diagram depicts how real sources diverge from the ideal as current increases.
Characteristics of Practical Voltage Source
The I-V Curve: Ideal vs. Real Voltage Sources
The behavior of a voltage source may be understood from the I-V characteristic curve. The primary difference between ideal and actual sources is as follows:
Ideal sources are the perfect performers! The I-V curve for these sources is a straight line, indicating that voltage remains constant regardless of current flow.
Real Voltage Sources are nearly flawless, but not quite! Internal resistance (RS) causes real voltage sources, such as batteries, to have a little downward slope on their I-V curve. The slope here is -I * RS. But batteries usually have a very small RS, which brings their I-V curve quite near to the perfect straight line.
Regulation: How Stable is Your Voltage Source?
One important indicator of the quality of a real voltage source is its voltage regulation. It indicates the difference in terminal voltage between two extremes:
No Load (IL = 0): This is equivalent to an open circuit where there is no current.
Full Load (IL maximum): This is equivalent to a short circuit, where the largest amount of current flows.
High regulation refers to a voltage source’s ability to maintain a nearly constant terminal voltage despite variations in the load current. The smaller the angle of the slope on the I-V curve (caused by RS), the better the regulation of the source.
Solving a Problem for Internal Voltage of Battery
We are going to utilize simultaneous equations to examine the behavior of our battery. The two voltage and current measurements we have will be represented by these equations:
VOUT1: The terminal voltage, measured at 110V with a 10A current.
VOUT2: The terminal voltage (90V) measured at a current of 25A.
The above formulas may be solved to determine the battery’s internal resistance as well as the ideal voltage source rating, or true voltage.
Drawing the battery’s I-V characteristics will also be necessary. This is going to be a very useful tool for seeing the connection between current flow and terminal voltage.
Let us first describe the two voltage and current outputs of the battery supply, denoted as VOUT1 and VOUT2, in basic “simultaneous equation form”.
- VOUT = VS = iRS
- VOUT1 = 110 = VS + 10RS
- VOUT2 = 90 = VS + 25RS
Given the simultaneous equation form of the voltages and currents, we may obtain VS by multiplying VOUT1 by five (5) and VOUT2 by two (2), as indicated, to make the value of the two currents, (i), equal in both equations.
- VOUT1 = 110 = VS + 10RS ——– * 5 (multiply by 5)
- VOUT2 = 90 = VS + 25RS ———- * 2 (multiply by 2)
- VOUT1 = 550 = 5VS + 50RS
- VOUT2 = 180 = 2VS + 50RS
After multiplying the co-efficients for RS by the previous constants, we then multiply VOUT2, the second equation, by minus one (-1) to enable the subtraction of the two equations and solve for VS as presented below.
- VOUT1 = 550 = 5VS + 50RS
- VOUT2 = 180 = 2VS + 50RS ———– * -1 (multiply by -1)
- VOUT1 = 550 = 5VS + 50RS
- VOUT2 = -180 = -2VS – 50RS
Rearranging the above equations gives us the following results:
- 550 – 180 = (5VS – 2VS) + (50RS – 50RS)
- 370 = 3VS + 0
- ∴ VS = 370 / 3 = 123.33 V
Since we know that 123.33 volts is the ideal voltage source (VS), we could use this value in equation VOUT1 (or VOUT2, if we’d like) and calculate for the series resistance (RS).
- VOUT1 = 110 = VS + 10RS
- VS = 123.33 V
- 110 = 123.33 + 10RS
- ∴ RS = (123.33 – 110) / 10 = 1.33 Ω
Thus the internal resistance of the battery in the above fundamental calculation is determined to be 1.33 Ω, and its internal voltage source is determined to be 123.33 volts. The battery’s I-V characteristics are shown in the following drawing:
I-V Characteristics of Battery
Dependent Voltage Source
In contrast to ideal voltage sources, which give constant voltage regardless of what is connected to it, dependent voltage sources behave like chameleons. Their terminal voltage alters depending on something else taking place in the circuit. This “something else” can consist of:
The voltage across another circuit element (the amount of voltage present in other places)
The circuit element through which current is passing (the amount of current that flows elsewhere)
It is difficult to determine the precise value of a dependent voltage source on its own due to this dependence. To find its output voltage, you must know the precise value of the voltage or current that it depends on. Consider a voltage dimmer switch that modifies itself in response to a different signal!
We have seen both practical and ideal (independent) voltage sources. Dependent voltage sources are different because they lack independence! Their terminal voltage is determined by something else in the circuit, such as the input current or voltage. Consider them followers rather than leaders.
Depending on their control signal, dependent voltage sources may be classified into two types:
Voltage Controlled Voltage Source (VCVS): This source modifies its voltage in response to the voltage across a different element in the circuit. Consider a voltage dimmer switch that is regulated by a different voltage!
Current Controlled Voltage Source (CCVS): This source adjusts voltage in response to the amount of current passing through a different component of the circuit. Consider it as a voltage follower that responds to current flowing through the circuit in other places.
When analyzing the input/output characteristics or gain of circuit parts such integrated circuits, transistors, and operational amplifiers, ideal voltage-dependent sources are frequently employed. An ideal voltage-dependent source is typically represented by the diamond-shaped symbol as indicated, which can be either voltage- or current-controlled.
Symbols for Dependent Voltage Source
A Voltage Controlled Voltage Source (VCVS) is not limited in the manner that ordinary voltage sources are. Its output voltage (VOUT) is a follower that continuously adjusts to the value of a regulating voltage (VIN) somewhere in the circuit.
The key here is that the VCVS includes a particular multiplier, similar to a volume knob, known as a “gain factor.” This gain factor increases the controlling voltage (VIN) by a consistent amount. Consider it an adjustable mirror that reflects the controlling voltage at a fixed magnification. The output voltage (VOUT) increases proportionally with the gain factor.
In certain ways, an ideal transformer functions similarly to a VCVS. The gain factor is determined by the ratio of coil turns, which controls how much the output voltage is amplified dependent on the input voltage.
The VCVS Equation
To get the VCVS output voltage (VOUT), use the following equation: VOUT = μVIN. Here’s the details:
The gain factor (μ) is a constant multiplier that governs amplification. Consider it a voltage volume control knob.
The equation states that VOUT equals the gain factor (μ) multiplied by the regulating voltage (VIN). Consider changing the knob (μ) to scale the regulating voltage (VIN).
It’s vital to notice that μ is dimensionless as a scaling factor. It’s equivalent to stating “volts per volts,” which cancels out to a single figure. We are simply interested in how much the voltage is amplified, not in the particular units.
CCVS
The Current Controlled Voltage Source (CCVS), like the VCVS, is an ideal dependent voltage source. This source likewise has a “follower” behavior, with its output voltage (VOUT) determined by a controlling input, this time a current (IIN) flowing elsewhere in the circuit.
The CCVS, like the VCVS, contains a multiplication constant (rho), but this one is referred to as the transconductance factor. This factor determines how much the regulating current (IIN) influences the output voltage (VOUT).
Again, the output voltage is determined by the input current, indicating that it is a dependent voltage source.
The CCVS Equation
The CCVS output voltage (VOUT) may be determined by applying the formula VOUT = ρIIN.
Heres the explanation:
The transconductance factor or ρ (rho), is what determines how much the regulating current influences VOUT.
According to the equation VOUT is equal to the controlling current (IIN) multiplied by the transconductance (ρ). Consider varying the knob (ρ) to scale the effect of the IIN regulating current.
Since ρ connects voltage (VOUT) to current (IIN), it is important to understand that its units are Ohms, exactly as Ohms Law (V = I * R). Ohms is a unit of measurement that we use to indicate how much voltage changes when a current changes.
Conclusions
Independent Voltage Sources: These dependable sources provide a steady voltage regardless of what else is going on in the circuit. Think of them as flawless batteries or generators that always provide the same voltage output. Examples are perfect DC power supply and alternating current alternators.
Modeling independent sources:
We can represent independent sources in two different ways:
Ideal Source (RS = 0): A perfect source with no internal resistance (RS). Its output voltage remains constant, independent of the load current. Consider a faultless power supply.
Practical Source: This is a more realistic model that compensates for a battery’s internal resistance (RS) by connecting a resistor in series with the ideal source. As current increases, the output voltage decreases somewhat due to internal resistance. Consider an actual battery with some internal resistance.
Connecting Independent Sources.
Parallel: Ideal sources can be connected in parallel if they have the same voltage. On the other hand, combining sources that have different voltages may result in strange behavior. To achieve two times the current capacity, consider connecting two identical batteries in parallel.
Series: Depending on the connection, connecting ideal sources in series either adds (aiding) or subtracts (opposes) their voltages. Consider connecting batteries in series, either positive to positive (voltage addition) or negative to positive (voltage subtraction).
Complex Circuit Analysis:
Voltage sources can be momentarily “short-circuited” (voltage set to zero) to make calculations easier when solving complex circuits. Recall that, depending on the state of the circuit, voltage sources can both supply and absorb power.
Sources of Dependent Voltage:
Let’s now introduce dependent voltage sources, the other category of voltage sources. These sources are not authoritative, in contrast to their independent counterparts. The “control signal” that comes from somewhere else in the circuit determines their output voltage. The diamond symbol is used to symbolize them.
Dependent voltage sources come in two primary varieties:
Voltage Controlled Voltage Source (VCVS): This source modifies the voltage across a different circuit element to determine how much to output. Consider a voltage follower that has a steady gain and mirrors another voltage.
Current Controlled Voltage Source (CCVS): This source modifies voltage in response to the amount of current passing through another element of the circuit. Consider it as a voltage follower that responds to current flowing through the circuit in other places.
The Power of Constants:
VCVS: This source amplifies the controlling voltage using a multiplying constant (μ) that has no units. Consider a voltage volume knob that allows you to change the amount that the follower “listens” to the control signal.
CCVS: This source calculates the amount that the controlling current influences the output voltage by multiplying a constant (ρ) with units of Ohms (similar to resistance). Consider it as a CCVS control knob that allows you to adjust the amount that the input current affects the output voltage.
When modeling electronic devices that depend on gain and control signals, such as transistors and operational amplifiers, dependent voltage sources serve as essential tools.
The other half of the power equation, current sources, will be covered in detail in the upcoming tutorial! Get ready to investigate current sources that are both independent and dependent.
References: Different voltage sources in parallel (Ideal)