How are these resistors in series and parallel - Page 1
Forum section: electronics / beginners

author: Freshman
author_rank: Regular Contributor
timestamp: April 04, 2024, 05:47:39 am
content: I was going through the biasing resistor calculation for RS-485 and can across this AppNote (https://www.renesas.com/us/en/document/apn/an1986-external-fail-safe-biasing-rs-485-networks).On page 3, you can see the Figure 2 and Equation 2.I just want to understand how the 2 RB resistors are considered to be in series and their final value is considered to be in parallel with RT2?A resistor is said to be in parallel when both is ends are connected to another resistor. But how are the two RB resistors considered to be in series? And their equvivalent resistance finally in parallel with RT2?Can someone explain?

author: Andree Henkel
author_rank: Regular Contributor
timestamp: April 04, 2024, 07:56:49 am
content: Figure 2 is obscured by the two resistors named Req.If you look at figure one, you first need to combine parrallel Rt1 and Rt2.Now clearly upper and lower Rb resistors are in series to another,there is just an additional third resistor (the parallel combination) in the chain.This is still valid, once you add the Req resistors.

author: Zero999
author_rank: Super Contributor
timestamp: April 04, 2024, 08:44:15 am
content: A potential divider can be modeled as a voltage source, with a series resistance equal to both of the resistors connected in parallel.Here's a simpler example.VIN= 5VR1 = 5k6R2 = 2k4VOUT= VIN*R2/(R1+R2) = 5*2.4/(5.6+2.4) = 1.5VROUT= (R1*R2)/(R1+R2) = (5.6k*2.4k)/(5.6k+2.4k) = 1.68k

author: golden_labels
author_rank: Super Contributor
timestamp: April 04, 2024, 07:21:54 pm
content: Freshman: the fragment discusses equivalent resistance as seen by the cable. It’s the same as with equivalent resistance inThevening’s theorem, just in this case we also don’t care about Vs:Zero999: what software are you using to draw these nice, crisp circuits?

author: Zero999
author_rank: Super Contributor
timestamp: April 05, 2024, 07:07:37 am
content: I did that drawing awhile ago, so I don't remember. It looks like a mixture of MS Paint and Crocodile Clips. . .My previous post is an extract from anold one. Many of my old schematics were done using a child's simulator program called Crocodile Clips, which were often modified with MS Paint to add symbols with the program lacked. Nowadays I mostly use LTSpice for my schematics, but still occasionally MS Paint and KolourPaint, and modified old Crocodile Clips schematics/symbols.

author: MrAl
author_rank: Super Contributor
timestamp: April 05, 2024, 09:40:12 am
content: Quote from: Freshman on April 04, 2024, 05:47:39 amHi,The short answer is, when calculating impedances voltage sources act like short circuits. Thus, in that circuit Vs is shorted to ground and that puts the other two resistors that are now in series also in parallel with RT2. That is because an ideal voltage source has an impedance of exactly zero Ohms, which means we effectively have a zero Ohm resistor in parallel with the two other resistors that are in series (which is the 2*RB part).The other way to look at it is the parallel resistance could be called the Thevenin equivalent resistance RTH.Also interesting is that an ideal current source has infinite impedance, and so the impedance of a current source in parallel with a resistor is just the value of that resistor and nothing else.Note that when nothing else is mentioned about the sources, voltage and current source are considered to be ideal.There are many, many consequences to linearity. That allows various equivalencies in a lot of circuits.The most famous are probably the Thevenin and Norton equivalents that can be worded as follows...A voltage source in series with a resistance is equivalent to a current source in parallel with a resistance.A current source in parallel with a resistance is equivalent to a voltage source in series with a resistance.These two mean we can simplify some circuits especially when we use both of these ideas.An example of a voltage divider with R1 and R2 and voltage source V:Here we have a voltage V in series with R1, then the current source becomes I=V/R1 in parallel with R1. Now if R1 is in series with R2 before we started with the other end of R2 connected to ground (the other terminal of the now current source), then now we have a terminal voltage:Vx=I*Rp (and recall I=V/R1)where Rp is the parallel combination of R1 and R2 which is R1*R2/(R1+R2).For example, if V=2 volts and R1 and R2 were both 2 Ohms, the current source would be:I=V/R1=V/2=2/2=1 ampand Rp would be 1 Ohm (R1 in parallel with R2).Since we now would have a current source of 1 amp in parallel with 1 Ohm, the terminal voltage would be 1 volt.Notice that's the same voltage as if we had a voltage divider with R1=2 and R2=2 and a voltage source of 2 volts and used the voltage divider formula:Vout=V*R2/(R1+R2)These kinds of equivalents allow circuits to be simplified, and simplifications were very important years ago before the age of computers. Today they are still useful in theoretical studies.

author: golden_labels
author_rank: Super Contributor
timestamp: April 05, 2024, 12:57:31 pm
content: And the associated illustration: