# Impedance matching

#### AndrieGnd

Joined Jun 25, 2019
52
Hi guys!
According to impedance matching in electronics for getting maximum power from the voltage's source, I'm totally convinced with Zs=ZL , (the circuit is about voltage source connected serial with Zs and Zs connected serial with ZL(ZL is the resistor on the load) ) , whenever I use impedance transformer, why can't I say that I want to match Zs with ZL(ZL is the load) ? we generally are saying we want to match resistor on the load with Zs , but the opposite is also works for this equation Zs=ZL , so we can connected the impedance transformer as "implicitly" the load now is Zs, and Zs exchanged with ZL; i.e now I have ZL connected serial with Zs(Zs is now connected as a load) ... can't I do that conclusion?! maybe because the transformer of impedances are one directional?!

I'm asking because it's weird we always want to match the load to the serial connected resistor and not the vise versa.

#### MrChips

Joined Oct 2, 2009
20,275
Not for maximum power.

Power = V x V / R

Hence for maximum power, ZL = 0.

When ZL is finite and non-zero, you want ZS = ZL .

• AndrieGnd

#### MrAl

Joined Jun 17, 2014
7,156
Hi guys!
According to impedance matching in electronics for getting maximum power from the voltage's source, I'm totally convinced with Zs=ZL , (the circuit is about voltage source connected serial with Zs and Zs connected serial with ZL(ZL is the resistor on the load) ) , whenever I use impedance transformer, why can't I say that I want to match Zs with ZL(ZL is the load) ? we generally are saying we want to match resistor on the load with Zs , but the opposite is also works for this equation Zs=ZL , so we can connected the impedance transformer as "implicitly" the load now is Zs, and Zs exchanged with ZL; i.e now I have ZL connected serial with Zs(Zs is now connected as a load) ... can't I do that conclusion?! maybe because the transformer of impedances are one directional?!

I'm asking because it's weird we always want to match the load to the serial connected resistor and not the vise versa.
Hi,

I think what you mean is maximum power *transfer*.

Max power transfer means you want the max power to go from the source to the load.
Maximum power by itself means you might be trying to draw the maximum power from the source with no regard for the load.

Max power transfer means you need ZL=ZS.
The simple example is when ZS is a resistor. Let's say it is 50 Ohms.
If ZL is less than 50 Ohms the current is higher but the voltage is lower so the voltage current product is lower.
If ZL is more than 50 Ohms then the voltage is higher but the current is lower so the voltage current product is lower.
If ZL is 50 Ohms then the voltage and current product is maximum for the load and so you get the most power from the source to the load.

A little proof:

The voltage on the load is Vx=Vs*RL/(RS+RL)
The current on the load is Ix=Vs/(RS+RL)
The power on the load is:Vx*Ix=(Vs^2*RL)/(RS+RL)^2
Taking the first derivative with respect to RL and setting it equal to zero we have:
(Vs^2*(RS-RL))/(RS+RL)^3=0
Solving for RL we get:
RL=RS
and this happens to be a maximum so we know RL must equal to RS.

• AndrieGnd