The well-known Kirchhoff’s current law is often used in linear circuit analysis. It’s also called Kirchhoff ’s first law, Kirchhoff ’s point rule, Kirchhoff ’s junction rule, and Kirchhoff ’s first rule. The law says that at any point in an electric circuit, the sum of currents flowing toward the point is equal to the sum of currents flowing away from the point. That is, the net current flow into the point is always zero.
This article describes a new way of using Kirchhoff’s current law to make circuit analysis clearer and simpler. For example, using the very simple example circuit in Figure 1, the current law says:
We can write the above equation as:
and rearrange it to:
Equation 3 is equivalent to Equation 1, but it could have different meanings. The left side of Equation 3 means currents flowing away from the point through resistors as if V1 and V2 are grounded. The right side means all currents flowing into the point as if the middle point is grounded. It’s much easier to write equations in this way. Another example involves equations for a differential amplifier (Fig. 2). Using the new method, we have:
Solving the above equations:
Extending this technique to a more complicated circuit (Fig. 3) leads to four equations for the four nodes:
Thus, the new technique for using Kirchoff ’s law generates equations that are simple and easy to use.
This idea seems innocent, but actually drives to the design of new algorithms for circuit simulation software to design integrated circuits with thousands nodes, in particular it drives to a simple, method to design millimeter wave filters with hundred poles over integrated circuits with hundreds of printed spiral inductors and comb capacitors forming fractal filters, thus giving very sharp spectral curves.
Jaime Soto Figueroa -July 19, 2008
The method presented is actually Millman's Theorem. If you divide both sides of equation 3 for example by ((1/R1)+(1/R2)), what you will obtain is the Millman's Theorem expression for the voltage at the node lower-case phi.
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Harry Moodie -June 16, 2008
Learned that 45 years ago when tinkering with electronics and it was an old hat then.
Maybe this simple analysis method has to be refreshed to electronic engineers of the digital-only age. Nothing wrong with that. But don't call it "NEW".
Gerd Rosenbaum -June 04, 2008
Kirchhoff Junior missed the point. The point is that the output of any linear circuit can be calculated as the superposition (or sum) of the outputs obtained by setting each input one at a time to its input value while setting all other inputs to zero. If the circuit has an output with all inputs set to zero, then that output value must also be included in the sum. This often greatly simplifies the math, and allows a solution largely by inspection. For example, in figure 2, setting V2 = 0, we get V0 = -(R2/R1) * V1. Setting V1 = 0, we get V0 = V2 * (R4/(R3+R4)) * (1+R2/R1). Adding these two terms together gives equation 6, with almost no math required.
Don Patterson -May 30, 2008
I cannot see anything new in this method! As much as I can see from the article that is well known node potential method - as old as electrical engineering and can be found in many text book!
Kirchhoff Junior -May 26, 2008
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