Zach has a new stream "Getting Started with an nRF52 Series MCU", but I did not post my thoughts on matching the nRF52 with a 50 ohm antenna there. Let's try to match the nRF52840 to the antenna using Zach's method and formula, as I did for the ESP32-S3 chip. The antenna output impedance of the nRF52840 will be taken as Zl = (35 - i*35). This average impedance of the nRF52840 can be obtained from the file "nRF52840 QIAAC0 matching network.s2p" for frequencies close to 2.4 GHz. that is | Zl | = 50, Zlr = 35, Zli = -35 That is, for the first L/8 section that comes out of the nRF52840, the impedance will be equal to Z1 = | Zl | = 50 Ohm. According to Zach's formula: Zin (real) = | Zl |^2 * (2* Zlr)/((| Zl | - Zli)^2 + Zlr^2) we get: Zin (real) = 50^2 * (2*35) / ((50 - (-35))^2 + 35^2) Zin (real) = 20,7 Ohm Then for the second section L/4, which comes immediately after L/8, the impedance will be equal to: Z2 = square root (50 * Zin) = square root (50 * 20,7) Z2 = 32,2 Ohm So, to match the nRF52840 with a 50 ohm antenna using Zach's “L/4 + L/8” method, we get that: - the L/8 line segment must be 50 Ohm, and - the next L/4 segment must be 32.2 Ohm.
It is necessary to continue the calculations given by Zach. After all, we still haven't worked out the equation for Zin. Let's use the same trick that Zach gave, assume that the load impedance (Zl) is: Zl = Zlr + i*Zli (1) For a line Z1 of length equal to lambda/8, we have an expression for the input impedance: Zin = Z1 * (Zl + i*Z1)/(Z1 + i*Zl) But since Z1 = | Zl |, we get: Zin = | Zl | * (Zl + i*| Zl |)/(| Zl | + i*Zl) (2) Let us replace Zl in expression (2) with the equivalent from (1): Zin = | Zl | * ((Zlr + i*Zli) + i*| Zl |)/(| Zl | + i*(Zlr + i*Zli)) Zin = | Zl | * (Zlr + i*(Zli + | Zl |))/((| Zl | - Zli) +i*Zlr) After reducing the denominator to a real number, we get the final Zach’s formula for his matching method “L/4 + L/8”: Zin (real) = | Zl |^2 * (2* Zlr)/((| Zl | - Zli)^2 + Zlr^2) (3) Let's check the formula for Z1 of length equal to lambda/8 with the load impedance (25 - i*7): that is | Zl | = 26, Zlr = 25, Zli = (-7) Z1 = | Zl | = 26 Ohm (this will be the characteristic impedance for the line L/8) Zin (real) = 26^2 * (2*25) / ((26 - (-7))^2 + 25^2) Zin (real) = 19,7 Ohm Let's look at what happens if we apply Zach's method and formula to match the ESP32-S3 chip to the stated impedance (35+j10). That is, we will be able to match a 50 ohm antenna with this chip without using lumped components. that is | Zl | = 36,4, Zlr = 35, Zli = 10 Z1 = | Zl | = 36,4 Ohm (this will be the characteristic impedance for the line L/8) Zin (real) = 36,4^2 * (2*35) / ((36,4 - 10)^2 + 35^2) Zin (real) = 48.3 Ohm Сharacteristic impedance Z2 for the line L/4 is: Z2 = square root (50 * Zin) = square root (50 * 48.3) Z2 = 49,1 Ohm (this will be the characteristic impedance for the line L/4)
Thanks for all the information been watching all these videos ! wish these videos existed back when I was in uni they are so helpful.
Glad you like them!
Zach has a new stream "Getting Started with an nRF52 Series MCU", but I did not post my thoughts on matching the nRF52 with a 50 ohm antenna there.
Let's try to match the nRF52840 to the antenna using Zach's method and formula, as I did for the ESP32-S3 chip.
The antenna output impedance of the nRF52840 will be taken as Zl = (35 - i*35). This average impedance of the nRF52840 can be obtained from the file "nRF52840 QIAAC0 matching network.s2p" for frequencies close to 2.4 GHz.
that is | Zl | = 50, Zlr = 35, Zli = -35
That is, for the first L/8 section that comes out of the nRF52840, the impedance will be equal to Z1 = | Zl | = 50 Ohm.
According to Zach's formula:
Zin (real) = | Zl |^2 * (2* Zlr)/((| Zl | - Zli)^2 + Zlr^2)
we get:
Zin (real) = 50^2 * (2*35) / ((50 - (-35))^2 + 35^2)
Zin (real) = 20,7 Ohm
Then for the second section L/4, which comes immediately after L/8, the impedance will be equal to:
Z2 = square root (50 * Zin) = square root (50 * 20,7)
Z2 = 32,2 Ohm
So, to match the nRF52840 with a 50 ohm antenna using Zach's “L/4 + L/8” method, we get that:
- the L/8 line segment must be 50 Ohm, and
- the next L/4 segment must be 32.2 Ohm.
It is necessary to continue the calculations given by Zach. After all, we still haven't worked out the equation for Zin. Let's use the same trick that Zach gave, assume that the load impedance (Zl) is:
Zl = Zlr + i*Zli (1)
For a line Z1 of length equal to lambda/8, we have an expression for the input impedance:
Zin = Z1 * (Zl + i*Z1)/(Z1 + i*Zl)
But since Z1 = | Zl |, we get:
Zin = | Zl | * (Zl + i*| Zl |)/(| Zl | + i*Zl) (2)
Let us replace Zl in expression (2) with the equivalent from (1):
Zin = | Zl | * ((Zlr + i*Zli) + i*| Zl |)/(| Zl | + i*(Zlr + i*Zli))
Zin = | Zl | * (Zlr + i*(Zli + | Zl |))/((| Zl | - Zli) +i*Zlr)
After reducing the denominator to a real number, we get the final Zach’s formula for his matching method “L/4 + L/8”:
Zin (real) = | Zl |^2 * (2* Zlr)/((| Zl | - Zli)^2 + Zlr^2) (3)
Let's check the formula for Z1 of length equal to lambda/8 with the load impedance (25 - i*7):
that is | Zl | = 26, Zlr = 25, Zli = (-7)
Z1 = | Zl | = 26 Ohm (this will be the characteristic impedance for the line L/8)
Zin (real) = 26^2 * (2*25) / ((26 - (-7))^2 + 25^2)
Zin (real) = 19,7 Ohm
Let's look at what happens if we apply Zach's method and formula to match the ESP32-S3 chip to the stated impedance (35+j10). That is, we will be able to match a 50 ohm antenna with this chip without using lumped components.
that is | Zl | = 36,4, Zlr = 35, Zli = 10
Z1 = | Zl | = 36,4 Ohm (this will be the characteristic impedance for the line L/8)
Zin (real) = 36,4^2 * (2*35) / ((36,4 - 10)^2 + 35^2)
Zin (real) = 48.3 Ohm
Сharacteristic impedance Z2 for the line L/4 is:
Z2 = square root (50 * Zin) = square root (50 * 48.3)
Z2 = 49,1 Ohm (this will be the characteristic impedance for the line L/4)
Hi there could you share file?
upgraded! yay!