Why does smith chart show real value 1 when the reflection coefficient is zero ? - Page 1
Forum section: electronics / rf-microwave

author: electronic_guy
author_rank: Regular Contributor
timestamp: February 12, 2024, 06:10:57 am
content: Hi,On a smith chart with normalized reflection coefficient (Z_load/Z_characteristic_impedance), why does the normalized impedance becomes only real. There is no imaginary impedance value at the origin. What is the physical meaning of it ? I'm very new to this, please explain.Thanks

author: radiolistener
author_rank: Super Contributor
timestamp: February 12, 2024, 10:15:57 am
content: physical meaning is that 100% energy is consumed by load, so 0% energy is reflected back.

author: electronic_guy
author_rank: Regular Contributor
timestamp: February 13, 2024, 07:38:47 am
content: Why isn't there an imaginary value for that impedance ? The characteristic impedance of the transmission line could have been a complex value when it got matched with a load right ? The origin of the smith chart represents only a real value and the imaginary value is zero.

author: Andy Chee
author_rank: Super Contributor
timestamp: February 13, 2024, 07:49:19 am
content: If the inductive and capacitive reactances of the transmission line are equal, they will cancel out i.e. zero imaginary impedance.Obviously such cancellation is frequency dependent.

author: yl3akb
author_rank: Regular Contributor
timestamp: February 13, 2024, 08:28:13 am
content: Quote from: electronic_guy on February 13, 2024, 07:38:47 amThe center point is not impedance of transmission line, but point where impedance is perfectly matched (zero reflection). For perfect maximum power transfer match you always need to match real parts and cancel imaginary parts . It doesn't matter if Z of components involved in matching (like lossy transmission lines) themselves have imaginary parts.

author: Kalvin
author_rank: Super Contributor
timestamp: February 13, 2024, 09:34:30 am
content: The horizontal axis from left to right (the axis from short to open, ie. zero ohms to "infinite" ohms) is the line where the reactance part of the impedance is 0. The physical meaning is that if the impedance lies on this horizontal axis, the impedance is either purely resistive, or the inductive and capacitive reactance cancel out.

author: pdenisowski
author_rank: Super Contributor
timestamp: February 13, 2024, 09:53:22 am
content: Most popular of the > 200 videos I've made for R&S

author: radiolistener
author_rank: Super Contributor
timestamp: February 13, 2024, 10:26:02 am
content: Quote from: electronic_guy on February 13, 2024, 07:38:47 ambecause there is no reflectionQuote from: electronic_guy on February 13, 2024, 07:38:47 amNo. characteristic impedance of transmission line is a parameter of transmission line. It don't depends on the load.Quote from: electronic_guy on February 13, 2024, 07:38:47 amThe real value represents consumed energy part (for example it can be heat loss, radiation loss, etc).Imaginary value represents reflected energy part. (this part is not loss, it flows back and forth)Since it shows zero imaginary part, it means that there is no reflection.Matching means that you're adding conjugate component to block reflected energy returning back to the source. It leads to accumulate RF energy between matching circuit and load and then push it into the load again on the next oscillation cycle. It will be consumed by load due to higher amplitude or higher current. But some part will be lost in the transmission line due to heating.

author: RoGeorge
author_rank: Super Contributor
timestamp: February 13, 2024, 10:48:51 am
content: Quote from: electronic_guy on February 12, 2024, 06:10:57 amThe physical meaning is the phase shift between voltage and current. When the voltage and current through a load are perfectly in phase (phase shift zero), there is no imaginary part. Or else said, that is a resistive behavior.Image source:https://en.wikipedia.org/wiki/Electrical_impedanceIf you think about impedance as in the above plot, Z is the impedance, R is the resistive (real) part, X is the reactance, and Theta angle \$\Theta\$ is the phase shift between U and I.XL and XC (for ideal L or C) are always at 90 degree, so they point either up or down. An ideal resistor R can not introduce phase shifts, it's angle is always zero (horisontal). When different resistive values R (resistors) and reactance values X (capacitors or coils) are combined together, the result is a complex impedance Z as in the picture (those are all vectors, so X and R add up as the Z seen in the picture), and the resulting Theta angle will be different from just -90, 0 or +90, as if it were for a single ideal component. Which one is up and which one is down (XL or XC) might depend by convention (which is taken as reference, voltage or current), but usually we measure voltages, so XL is pointing up in that complex impedances plane (XL has positive sign), and XC is pointing down (negative sign) in the complex plane from the above picture.When we match impedances, we want something (either an L or a C) such that it compensates for the already existing X (being it up or down), such that the resulting Z is pure resistive (Theta zero). In other words, we want thecomplex conjugate, or much clear in physical meaning words, we want the opposite component:- If the behavior is capacitive, so an XC vector pointing down, we identify the XC vector lenght, and use an equal size vector pointing up, so we need a coil with an XL of the same length. The result is that they cancel each other, and there will be no phase shift between I and U. Already existing R vector will remain there, horizontally. The resulting circuit will behave as a pure resistor (the usual 50 ohms, but can be other values too).- there is another aspect, in case of 2 ideal resistive circuits, for maximum power transfer (or else said for zero energy reflected back), the two of source and load must have the same value. So the complete rule (in AC) for matching is to have complex conjugate impedances. If one is A+jB ohm, the other must be A-jB ohm, so according to that complex impedance plane posted above, when putting them together, +jB with -jB (the reactances) will cancel each other, and only the pure resistive part (A = A = 50) will remain.

author: xmo
author_rank: Regular Contributor
timestamp: February 16, 2024, 05:31:47 pm
content: I have been contemplating this discussion for a while and I think a little clarification might be helpful for future readers.The original post said: “On a smith chart with normalized reflection coefficient (Z_load/Z_characteristic_impedance)”The reflection coefficient is not (Z_load/Z_characteristic_impedance)The reflection coefficient of a termination is the ratio of the reflected voltage to the incident voltage.Accordingly, it can have a value from zero, which represents a reflectionless termination, to one, which represents a totally reflecting termination: a short, an open, or pure reactance.It is a vector quantity expressed in polar form as the magnitude of the reflection coefficient at an angle (theta). Γ = |Γ| ∡ΘThe angle (Θ) represents the phase difference between the reflected voltage and the incident voltage. The angle is positive when the reflected voltage leads the incident voltage in the case of a termination containing an inductive reactive component. Theta is negative when the reflected voltage lags the incident voltage in the case of a termination containing a capacitive reactive component.When plotting impedance, the center of the Smith chart represents a perfect match with a normalized impedance of 1.When plotting reflection coefficient, the center of the chart is the polar origin with a value of zero.Smith chart forms have two scales to assist with plotting a reflection coefficient point. One of the scales surrounding the circumference of the chart is labeled “Angle of Reflection Coefficient in Degrees” The reflection coefficient lies on a radius extending from the origin to the angle theta on this scale.The distance along the radius from the origin to the reflection coefficient point can be determined using the scale labeled “RFL COEFF” which is included with the “Radially Scaled Parameters” group at the bottom of the form.The attached image shows an example.Once a reflection coefficient point is plotted, the impedance of the load can be found as explained in the excellent video by pdenisowski