Understanding Current Sources with Calculations

Unlike voltage sources which focus on constant voltage, current sources are more concerned with ensuring a constant supply of current (amps). The current flow stays constant regardless of the voltage developed at their terminals (which is determined by other circuit components). Consider a water pump that continues to push a certain amount of water regardless of the pressure in the pipes.

Theoretically.. an ideal current source may provide an endless flow of energy, much like a magical pump with limitless power! Current sources are rated according to the amount of current they supply (3 amps, 15 amps), much like voltage sources have ratings (5V, 10V).

The primary distinction between voltage and current sources is their symbol. A current source has a circle with an arrow inside of it rather than just a plain circle. The direction of the constant current flow is shown by this arrow.

Current sources flow in the same direction as their positive terminal much like voltage sources do. Consider it as moving out from the positive side in the same direction as electrons. In circuits, current sources are frequently represented by the letter “i”.

Ideal Current Source

“Constant current source,” another name for an ideal current source truly embodies its meaning. Any device connected to it will always receive a constant current (amps) from it. This constant flow results in a straight line on the I-V characteristic curve (which depicts the relationship between current and voltage).

Similar to voltage sources, current sources can be:

• Independent (Ideal): These are the masters of constant-flow, delivering a constant current at all times.
• Dependent (Controlled): These modify their current in response to a signal from another part of the circuit that contains voltage or current. This signal may fluctuate over time or remain steady.

For circuit analysis, ideal independent current sources are great. They assist us with troubleshooting complex problems and debugging circuits that contain actual active components, such as transistors.

A resistor coupled in series with a voltage source is the simplest form of current source. Currents ranging from negligible milliamperes (mA) to hundreds of amps can be produced by this combination. Remember that a current source with zero current is equivalent to an open circuit with infinite resistance (R = 0). An open circuit cannot allow any current to pass through it.

Current Sources: Understanding the Flow

As seen by the arrow in their symbol, current sources are two terminal parts that allow current travel in a particular direction. The letter “i” in amps (often abbreviated as “amps”) represents their current value.

Ohm’s Law’s Relationship:

Ohm’s Law (V = I * R) describes the relationship between current sources and voltage in a circuit. In a circuit both voltage and current have specific values.

The Voltage Mystery

Determining the precise voltage across an ideal current source is more difficult than it is for voltage sources, particularly in complex circuits with several sources. Its supply of current (i) may be known to us but the voltage (V) across it is unknown.

If we know how much power (P) is given by the current source… we may solve for the unknown voltage (V) using the formula P = V * I. Consider power to be the missing component in solving the voltage problem.

Investigating the Mysteries of Voltage: Individual vs. Multiple Sources

Determining the voltage across a source of current can be difficult, particularly in complex circuits. Here’s how it breaks down:

Single Source: It is simpler to identify the voltage polarity (positive or negative) if it is the single source in the circuit.

Many Sources: When there are several sources things become more complicated. The voltage across the current source is determined by how it connects to the remaining portion of the circuit (the network).

Connecting current sources is similar to adding or subtracting water flow.

Ideal current sources can be connected together much like voltage sources. This may increase the total available current (as in adding water flow) or lower it (as in closing water flow). Nevertheless, depending on whether they are connected in series or parallel, there are certain guidelines for connecting several current sources with various values. Next, we’ll look at these guidelines!

Current Source in Parallel

Combining Current Sources: Parallel Electricity

To increase the overall current flow we might connect ideal current sources in parallel, just like we would with batteries.

When two or more current sources are connected in parallel, they become one current source, and the total current output of that source is equal to the sum of the algebraic currents from each source. Two 3 amp current sources are coupled in this example to provide 6 amps.

The equation illustrates that the total current (I_T) is equal to the sum of the individual currents (I₁ and I₂) from each source:

I_T = I₁ + I₂

The current source arrows, which show the direction of flow, must point in the same direction for this addition to function. Imagine them both exerting the same force to push water in one direction.

Connecting current sources in parallel with opposite arrows (parallel-opposing) is conceivable, but it’s not optimal for circuit analysis. The total current in this instance is the difference between the different currents, similar to deducting the water flow from each pump separately.

Parallel Opposing Current Sources

Subtraction in Action: Parallel-Opposing Connection (although Not Advised)

Although we looked at parallel-aiding connections for increasing current, parallel-opposing connections are another method of connecting current sources in parallel. Here’s where things get interesting:

Current sources connected in parallel with opposing arrows have currents that subtract from one another when they are subtracted from one another. Envision a closed loop with two water pumps (current sources) pumping water in opposing directions.

According to the equation, the net flow (I_T) equals the difference between the individual currents (I₁ and I₂).

I_T = I₁ – I₂ (where I₁ is the larger current)

As an illustration, if two current sources, one with 5 amps (I₁) and the other with 3 amps (I₂), were connected in opposite directions, the net current (I_T) would be two amps (5A – 2A = 3A). In the closed loop, the bigger current (5A) effectively “overpowers” the lower current (2A).

Please Note: Connecting ideal current sources in parallel-opposing configurations is mathematically feasible but it is typically not recommended for circuit analysis. This is due to the fact that indefinite current can potentially be supplied by ideal current sources. This design may result in unexpected behavior and possible component damage in actual circuits with limitations.

Series Connection Prohibited:

As was previously indicated, it is neither permitted nor regarded as best practice to connect ideal current sources in series. In later talks we’ ll go into the rationale behind this restriction.

Current Sources in Series

Ideal current sources should never be connected in series in circuit analysis, unlike batteries, which increase voltage when connected in series. This is the reason why:

The Unpredictable Result: Assume that two identical 3 amp current sources are connected in series. Would you receive 3 or 6 amps? Unfortunately, we are unsure of the exact solution! Circuit analysis becomes unclear when ideal current sources are connected in series.

Violating the Laws of Current Flow: Ideal current sources are made to keep a steady current flowing regardless of voltage. This flow is disrupted when they are connected in series because the total voltage across them becomes erratic. Consider two current sources, or water pumps, attempting to force water through a single pipe, or series connection. The water’s (current’s) direction of flow becomes unclear.

No Series-Aiding or Opposing: Adding or removing currents is a common practice in series connections. Ideal current sources, on the other hand, always push current in the direction that their arrow points. With them, the notion of “series-opposing” or “series-aiding” does not exist.

Solving a Current Source Problem

Lets look at a circuit with two current sources connected in parallel-aiding arrangement! The parameters are given below:

Components:

Two current sources:

• I₁ = 200 milliamps (mA)
• I₂ = 100 milliamps (mA)

Load resistance: R = 20 ohms (Ω)

Problem:

• Calculate the total current delivered to the load (I_T).
• Find the voltage drop (V_R) across the load.
• Determine the power dissipated (P_R) in the load resistor.
• Draw a schematic diagram of the circuit.

Solution:

1. Total Current (I_T):

In parallel-aiding configuration, currents from both sources add up.

I_T = I₁ + I₂ = 200 mA + 100 mA = 300 mA

2. Voltage Drop (V):

We can use Ohm’s Law (V = I * R) to find the voltage drop across the load:

VR = IT * R = 300 mA * 20 Ω = 6 volts (V)

3. Power Dissipated (PR):

Another application of Ohm’s Law helps us calculate the power dissipated in the resistor:

P_R = V² / R = (6 V)² / 20 Ω = 1.8 watts (W)

Understanding Practical Current Sources

We looked at ideal current sources that, under any circumstances, miraculously produce a constant current. However things become a little more realistic (and less ideal) in the real world. This is the reason why:

Ideal vs. Practical: Ideal current sources possess infinite internal resistance (R = ∞). This means that they can potentially provide the same current indefinitely, regardless of the voltage at their terminals. Though this is a terrific way to conceptualize circuit analysis, its not precisely how things function in practice.

The Reality Check: Practical current sources are always constrained by their internal resistance (R_p), which is never genuinely infinite. This internal resistance does not go away even at very high values (typically in the mega-ohm range). Because of this internal resistance the actual current output varies significantly based on the associated load resistance.

Modeling Real World Situations: An ideal current source with its internal resistance (R_p) connected in parallel (like a shunt) across it can be used to represent real-world situations. Keep in mind that parallel components undergo the same voltage loss.

The ideal constant current flow can be basically stopped by the internal resistance of a practical current source. More internal resistance means that the actual current output will stray less from the  ideal value.

Ideal and Practical Current Source

The Norton Connection:

Astute observers may have noticed that practical current sources have a striking resemblance to a Norton equivalent circuit. Do you recall Norton’s theorem… It states that an ideal current source (I_S) connected in parallel to a resistor (R_P) may be used to substitute any DC circuit.

The Effect of Internal Resistance (R_P): The internal resistance of the real current source is represented by this parallel resistor (R_P).

Extremely Low R_P (Shorted): The current source effectively functions as a dead end if R_P is extremely close to zero (think short-circuited). There is no current passing through it.

Extremely High or Infinite R_P (Ideal): In contrast, if R_P is very high, that is, getting close to infinity, it functions similarly to an open circuit. We simulate an ideal current source as having no resistance to obstruct the flow.

The I-V characteristic: Not as perfect as it once was

As we previously seen, the I-V characteristic curve, which plots current against voltage, exhibits a flat, horizontal line for an ideal current source. The problem with practical sources, though, is this:

Internal Resistance Takes Center Stage: An effective source’s internal resistance (R_P) functions similarly to a cunning thief. It diverts some of the current away from the ideal output.

The Slanted Line: The I-V characteristic of a practical source is no longer a perfect horizontal line due to the current being diverted by R_P. Rather, it has a small downhill slope. Imagine that the entire current splits into two paths: one that passes through the internal resistance (R_P) and the other that passes through the load. The overall output current somewhat decreases as the voltage across the source rises because more current is “stolen” by the internal resistance.

Internal Resistance’s Effects on Current, Voltage, and KCL

We have learned how voltage, current, and resistance are related by Ohm’s Law (V = I * R). Let’s now investigate its application to real-world current sources that include internal resistance (R_P):

Internal Resistance and Voltage Drop: Do you recall Ohm’s Law? It also holds true for internal resistance, or R_P. There is a voltage drop (i * R_P) across RP when current (i) passes through it. The source’s ideal current output (I_S) is decreased by this voltage drop.

Ideal Case: Zero Voltage Drop: There is no voltage drop across the internal resistance (i * R_P = 0) with an ideal current source (with infinite internal resistance, R_P ≈ ∞). Because there is no internal resistance to cause a drop, this also means that the output voltage (V_OUT) is zero.

The Application of Kirchhoff’s Current Law (KCL)

According to KCL, the total current flowing into and out of a junction has to be equal. Let’s use the practical current source as an example:

Output Current (I_OUT): This is the current that flows from the source to the load.

KCL Equation: I_S – V_S/R_P = I_OUT. In this case, RP stands for internal resistance, VS for voltage across the source terminals, and I_S for ideal current source value.

The I-V Characteristic Is No Longer a Flat Line

The I-V characteristic (current vs. voltage) of a real-world current source may be graphed using this KCL equation. What we receive is as follows:

Sloped Line: The I-V characteristic of a practical source is a straight line with a negative slope of -R_P, in contrast to the ideal situation, which is a flat line. The slope represents the amount that the current output (I_OUT) drops as the voltage (V_S) rises.

Interestingly, the I-V line meets the vertical voltage axis at the same location as the ideal current value (I_S) when the source is ideal (R_P ≈ ∞). This makes sense as the ideal current flows out in its entirety in the absence of internal resistance.

I-V Characteristics of Practical Current Sources

Parallel to the voltage axis, the I-V characteristic is a straight line, indicates an output of constant current, independent of the voltage across its terminals.

An inclined line that deviates from the ideal situation is the I-V characteristic.

The equation V_OUT/R_P yields the slope, where:

V_OUT stands for the source’s output voltage.

RP stands for the source’s internal parallel resistance.

The downward slope in the I-V characteristic is caused by internal resistance (R_P), which produces a voltage drop that lowers the ideal current output.

Solving a Practical Current Problem

We have the following details

• A practical current source is constructed with:
• Ideal current source: 2 Amps (A)
• Internal parallel resistance: 400 Ohms (Ω)
• No load is attached to the source.

Calculate the open-circuit terminal voltage (V_RP) of the current source. Determine the no-load power absorbed by the internal resistor.

1. When no load is attached

• I_S = I_R = 2 A, R_P = 400 Ω
• V_AB = V_RP = IS * R_P
• ∴ V_RP = 2 * 400 = 800 or 0.8 kV
• P_R = I²S * R_P
• P_R = 2² * 400 = 1600 W or 1.6 kW

Thus, 800 volts (or 0.8 kV) is the predicted open circuit voltage between terminals A and B (V_AB) and the internal source resistance.

Part 2: If the A and B terminals of the same practical current source are connected to a 250 Ohm load resistor. Determine the voltage drop across the load resistor, the power absorbed by each resistance, and the current passing through each resistance. Sketch the circuit that results from it.

Data that we have with load connected are: I_S = 2 A, R_P = 400 Ω and R_L = 250 Ω

We may apply the current-division rule to determine the currents in each resistive branch.

• I_RP = [R_L / (R_P + R_L)] * I_S
• = [250 / (400 + 250)] * 2
• = 0.76 A
• I_RL = [R_P / (R_L + R_P)] * I_S
• = [400 / (250 + 400)] * 2
• = 1.23 A
• ∴ I_RP + I_RL
• = 0.76 + 1.23
• = 2 A = I_S

Now to calculate power absorbed by each resistor we can use the following formula:

• P_RP = I²_RP * R_P
• = 0.76² * 400
• = 231.04 W
• P_RL = I²_RP * R_L
• = 1.23² * 250
• = 378.22 W

Consequently, we can calculate the voltage drop across the load resistor, R_L as shown below:

• V_AB = I_S * R_T
• R_T = (R_P * R_L) / (R_P + R_L)
• = (400 * 250) / (400 + 250)
• = 153.84 Ω
• ∴ V_AB = 2 * 153.84
• = 307.68 V

Fascinating information In theory, an open practical current source can sustain its rated current by producing an extremely high voltage, in the above example, 800 volts. If possible, this voltage may even be infinite.

On the other hand, attaching a load, such as a resistor, creates a path for the current. In the above case, the voltage dips to 307.68 volts when there is a load. This demonstrates that the voltage across the terminals for sources of continuous current is exactly proportional to the load resistance (greater resistance, higher voltage).

When connecting multiple sources in parallel that have internal resistance, such as the one we examined, their internal resistances add up in the same way as conventional resistors in parallel.

Dependent Current Source

We have looked at ideal current sources that function independently and always supply a constant current. Dependent current sources, however, are a different kind.

Independent (Ideal): Ideal current sources are self-contained, delivering a constant current independent of voltage or circuit.

Dependent: Dependent current sources are more collaborative than independent ones. A different element in the circuit determines their output current.

Responding to voltage or current: This different element in the circuit could be as follows:

Voltage Controlled Current Source (VCCS): The current output varies depending on the voltage across a different element or another element in the circuit.

Current Controlled Current Source (CCCS): The current output varies according on the current passing through another element.

Diamond Symbol: These dependent current sources are often represented by a diamond-shaped symbol with an arrow pointing in the current direction.

Dependent current sources function much like sensors in that they change their current output in response to changes in the voltage or current they sense in the circuit.

Symbols for Dependent Current Sources

Based on the regulating input voltage (V_IN), an ideal voltage-controlled current source (VCCS) modifies its output current (I_OUT).

The output current (I_OUT) varies in direct proportion to the voltage (V_IN). The equation I_OUT = α * V_IN, where α (alpha) is a constant known as the transconductance, represents this relationship.

In order to express how a change in voltage affects the current output, α is measured in amperes/volt (A/V).

An ideal current-controlled current source (CCCS) adjusts its controlling input current (IIN) in order to alter its output current (IOUT).

The output current (I_OUT) varies more with increasing controlling current (IIN). The relationship may be observed by the equation I_OUT = β * IIN, where β (beta) represents the constant known as the current gain.

Since it expresses the amount that the output current is scaled in relation to the input current, the unit of β is only a ratio with no dimensions.

Briefly put, CCCS reacts to current commands, whereas VCCS listens for voltage commands. Controlling currents depending on other circuit elements is made possible by these dependent current sources, which increase circuit design versatility.

Conclusion

From the above tutorial we learned a lot about current sources, both ideal and practical. Here’s a summary of the main points:

Ideal Current Sources:

Regardless of the voltage or the associated load, these ideal sources offer a constant current. Their I-V characteristic curve would look like a straight horizontal line as a result.

For circuit analysis, ideal sources function effectively when they are parallel (opposing or aiding). It is not recommended to link them in series, though.

For the purpose of applying theorems during analysis, current sources are regarded as open circuits (zero current). Depending on the circumstance, they can also function as power sources or sinks.

Practical Current Sources

Practical current sources, in contrast to their ideal counterparts, have a finite internal resistance (although a very large one, R ≈ ∞). As a result, its I-V characteristic curve has a decreasing slope. The current output somewhat reduces as the load (resistance) lowers.

An ideal source with an internal resistance connected in parallel (like a shunt) can be used to represent a practical source.

Dependent Current Sources

The dependent source is a different kind of current source. Based on another voltage or current signal somewhere else in the circuit, these sources adjust the output current.

There are two primary kinds:

Voltage-Controlled Current Source (VCCS): A controlling voltage is used to alter the output current.

Current-Controlled Current Source (CCCS): A controlling current determines how much the output current changes.

Electronic circuit analysis and design benefit greatly from the use of constant current sources with large internal resistances. They may be constructed with a variety of components, such as bipolar transistors, diodes, and FETs, either alone or in combination.

References: Calculating the power supplied by the current and voltage sources

Current source