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Characteristic impedance

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hamed333

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Hi, I want to know that what is the relation between Characteristic impedance and electrical length of microstrip line? I need a formula to show that they have a relation with each other.
 

Thanks, but I have seen in many papers of power dividers, there are relations between the Characteristic impedance and the electrical length of microstrip lines of their structure like this paper, the title of paper is: "Compact Microstrip Wilkinson Power Dividers
With Harmonic Suppression and Arbitrary
Power Division Ratios" you can see that in this paper Zo1 has the relation with its' electrical lenght!
 

hamed333 said:
Thanks, but I have seen in many papers of power dividers, there are relations between the Characteristic impedance and the electrical length of microstrip lines of their structure like this paper, the title of paper is: "Compact Microstrip Wilkinson Power Dividers
With Harmonic Suppression and Arbitrary
Power Division Ratios" you can see that in this paper Zo1 has the relation with its' electrical lenght!
Click to expand...

The characteristic impedance is defined by the propagation mode on a transmission line, and line cross-section geometry. Typical coaxial lines and striplines transmit TEM mode and their geometry is adjusted e.g. to 50 Ohms with which signal generators and loads operate. Different modes and geometries exist in waveguides.

Electrical length is defined by signal wave length on a transmission line which is mostly affected by the dielectric used in line supports. With vacuum or air the elecrical length may be close to open-air length with TEM mode while striplines supported by a dielectric (also coaxial cables) offer wave (and electric length) shortened by SQR(k), where k is dielectric permittivity.
 
Below follow a link the Microstrip N-Way Power Divider Calculator.

https://www.pasternack.com/t-calculator-nway.aspx

The microstrip wavelength, simply put, is the wavelength of the input signal as it is changed by the effective dielectric constant of the microstrip. This change-in-wavelength calculation is the same as it is in TEM (Transverse Electromagnetic Mode) applications, but because of the microstrip's properties, the "effective" dielectric constant must be calculated first.

The microstrap circuit are build by capacitor, inductor and resistor working in microwave can simulate:
- Impedance matching
- Attenuators
- Band Pass Filter
- High Pass Filter
- Low Pass Filter
- Butterworth Filter
 
λ=c/f Normally mismatch terminations to impedance controlled lines must not exceed 5~10% of λ.

c is reduced to 66~80% of freespace velocity due to dielectric constant relative to air and unless requested to be tested by board shop may have ~20% tolerance typ. for a fee.

The velocity of wave propagation in space is predicted by 1/sqrt(u * e) where 'u' and 'e' are the permeability and permittivity of medium.

My rule of thumb for FR4 is when track width is twice gap, it may be ~ 50 Ohms.
and 1/4 wavelength impedance inversion applies @80% of c.
Rogers, ceramic, polyamide, etc will each be different , value of e,, which tends to lower with rising GHz so beginners often underestimate this characteristic.
 
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