ZekeR
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Hello Friends,
Went back and looked at Middlebrook's EET (as described by Vorpérian in Fast Analytical Techniques for Electrical and Electronic Circuits). Read through the derivation, and I can see how he arrived at the answer,
\[H=H_o\frac{1+\frac{Z_N}{Z}}{1+\frac{Z_D}{Z}}\]
Where Z is the impedance of the added element; Ho is the original transfer function with the element removed and open-circuited; Zn is the output nulling impedance; and Zd is the driving point impedance.
And, like anything with electricity, there's a dual:
\[H=H_o^'\frac{1+\frac{Z}{Z_N}}{1+\frac{Z}{Z_D}}\]
where Ho' is a different version of the original transfer function with the element short-circuited instead of left open.
There's lots of math, a bunch of equations, and some derivation performed. And the math seems to work. However, I'm left unsatisfied... I'd like to have an intuitive explanation, and I don't have one yet.
For example, with KVL and KCL the explanation is pretty obvious: sum the voltages around a loop and you'll get zero (because energy is conserved), and whatever currents go into a node must come out (because charge is conserved). Nodal and loop analysis are pretty easy to grasp too: solve equations of KCL using variables of voltage, or solve equations of KVL with variables of current. It doesn't take more than a sentence to explain the procedure or why it's done that way, and the explanation is in plain English, not math.
For the EET, however, the explanation I can make (so far) is not in plain English; even if we add nulling impedance and driving point impedance to our vocabulary, the best explanation I can give is: "Multiply the original transfer function [with the extra element open-circuited] by the ratio of the sum of the added impedance and the nulling impedance over the sum of the added impedance and the driving point impedance." In other words, the explanation is an equation, which means it's not really an explanation. Oh, and if the original transfer function has the element short-circuited, then the equation changes. This is definitely not plain English, and it's easy to forget what goes where in the equation—and therefore, it's not very handy when you need it in a pinch.
So my question is this: Is there an intuitive and easy explanation in a spoken language for the EET? If you use the EET, are there any jingos or simplifications that you use to help you remember, understand, or apply it? How many forum members find the EET useful?
Went back and looked at Middlebrook's EET (as described by Vorpérian in Fast Analytical Techniques for Electrical and Electronic Circuits). Read through the derivation, and I can see how he arrived at the answer,
\[H=H_o\frac{1+\frac{Z_N}{Z}}{1+\frac{Z_D}{Z}}\]
Where Z is the impedance of the added element; Ho is the original transfer function with the element removed and open-circuited; Zn is the output nulling impedance; and Zd is the driving point impedance.
And, like anything with electricity, there's a dual:
\[H=H_o^'\frac{1+\frac{Z}{Z_N}}{1+\frac{Z}{Z_D}}\]
where Ho' is a different version of the original transfer function with the element short-circuited instead of left open.
There's lots of math, a bunch of equations, and some derivation performed. And the math seems to work. However, I'm left unsatisfied... I'd like to have an intuitive explanation, and I don't have one yet.
For example, with KVL and KCL the explanation is pretty obvious: sum the voltages around a loop and you'll get zero (because energy is conserved), and whatever currents go into a node must come out (because charge is conserved). Nodal and loop analysis are pretty easy to grasp too: solve equations of KCL using variables of voltage, or solve equations of KVL with variables of current. It doesn't take more than a sentence to explain the procedure or why it's done that way, and the explanation is in plain English, not math.
For the EET, however, the explanation I can make (so far) is not in plain English; even if we add nulling impedance and driving point impedance to our vocabulary, the best explanation I can give is: "Multiply the original transfer function [with the extra element open-circuited] by the ratio of the sum of the added impedance and the nulling impedance over the sum of the added impedance and the driving point impedance." In other words, the explanation is an equation, which means it's not really an explanation. Oh, and if the original transfer function has the element short-circuited, then the equation changes. This is definitely not plain English, and it's easy to forget what goes where in the equation—and therefore, it's not very handy when you need it in a pinch.
So my question is this: Is there an intuitive and easy explanation in a spoken language for the EET? If you use the EET, are there any jingos or simplifications that you use to help you remember, understand, or apply it? How many forum members find the EET useful?
