A tuning circuit using two inductively-coupled windings can readily effect an impedance transformation like a transformer. The coupling may be fixed or variable. Moving a tap on the output coil changes the turns ratio and permits raising or lowering impedance.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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A simple series L-C network is one of the ways to couple a random-length antenna, whose impedance can be quite unpredictable, directly to a transmitter. Other options include the L and Pi networks.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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A resonant vertical ground plane antenna offers an impedance in the range 30 to 50 ohms. A low-pass "L" network (series inductor followed by parallel capacitor) is commonly used with a high impedance random wire. With only two variables components, an "L" network has a limited range of impedance transformation. [ In reality, four "L" configurations are possible, two of which can match to a lower impedance. ]

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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The "Pi" configuration, usually an input shunt capacitor, a series inductor and an output shunt capacitor, resembles two L networks back-to-back. The Pi has greater impedance transformation range than the L network.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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The "Pi" configuration, usually an input shunt capacitor, a series inductor and an output shunt capacitor, resembles two L networks back-to-back. The Pi has greater impedance transformation range than the L network.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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With only two variables components, an "L" network has a limited range of impedance transformation. The "Pi" configuration, usually an input shunt capacitor, a series inductor and an output shunt capacitor, resembles two L networks back-to-back. The Pi has greater impedance transformation range than the L network. The "Pi-L" network, where the Pi output capacitor doubles as an input capacitor to a subsequent L section, provides even more harmonic suppression and a greater transformation ratio.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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With only two variables components, an "L" network has a limited range of impedance transformation. The "Pi" configuration, usually an input shunt capacitor, a series inductor and an output shunt capacitor, resembles two L networks back-to-back. The Pi has greater impedance transformation range than the L network. The "Pi-L" network, where the Pi output capacitor doubles as an input capacitor to a subsequent L section, provides even more harmonic suppression and a greater transformation ratio.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Within the context of matching the line to a transmitter, the goal is to present a suitable resistive impedance to the final amplifier. Impedance comprises a reactive value and a resistive value. To achieve matching, reactance must be cancelled and resistance transformed.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Key words: MULTIBAND ANTENNA. Such an antenna may radiate harmonics more readily. The added harmonic suppression of the "Pi-L" network is advantageous.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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With only two variables components, an "L" network has a limited range of impedance transformation. The "Pi" configuration, usually an input shunt capacitor, a series inductor and an output shunt capacitor, resembles two L networks back-to-back. The Pi has greater impedance transformation range than the L network. The "Pi-L" network, where the Pi output capacitor doubles as an input capacitor to a subsequent L section, provides even more harmonic suppression and a greater transformation ratio.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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"The Smith chart, invented by Phillip H. Smith (1905�1987), is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and matching circuits. (...) The Smith chart is most frequently used at or within the unity radius region. However, the remainder is still mathematically relevant, being used, for example, in oscillator design and stability analysis". (Wikipedia)

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Line lengths that are multiples of a half-wavelength replicate the load impedance at the input regardless of the Characteristic Impedance: i.e., the input impedance equals the load impedance. Line lengths that are odd multiples of a quarter-wavelength behave as impedance transformers. Quarter-wavelength line sections are said to invert impedance: an open is reflected as a short and vice-versa. When used for matching right at the antenna, a quarter-wavelength line section is called a "Q Section" or "Quarter-Wave Transformer".

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Line lengths that are multiples of a half-wavelength replicate the load impedance at the input regardless of the Characteristic Impedance: i.e., the input impedance equals the load impedance. Line lengths that are odd multiples of a quarter-wavelength behave as impedance transformers. Quarter-wavelength line sections are said to invert impedance: an open is reflected as a short and vice-versa. When used for matching right at the antenna, a quarter-wavelength line section is called a "Q Section" or "Quarter-Wave Transformer".

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Line lengths that are multiples of a half-wavelength replicate the load impedance at the input regardless of the Characteristic Impedance: i.e., the input impedance equals the load impedance. Line lengths that are odd multiples of a quarter-wavelength behave as impedance transformers. Quarter-wavelength line sections are said to invert impedance: an open is reflected as a short and vice-versa. When used for matching right at the antenna, a quarter-wavelength line section is called a "Q Section" or "Quarter-Wave Transformer".

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Line lengths that are multiples of a half-wavelength replicate the load impedance at the input regardless of the Characteristic Impedance: i.e., the input impedance equals the load impedance. Line lengths that are odd multiples of a quarter-wavelength behave as impedance transformers. Quarter-wavelength line sections are said to invert impedance: an open is reflected as a short and vice-versa. When used for matching right at the antenna, a quarter-wavelength line section is called a "Q Section" or "Quarter-Wave Transformer".

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Velocity Factor is a ratio of wave travel speed on a transmission line with respect to wave speed in vacuum. It is expressed as a percentage or a decimal fraction because waves travel slower on lines than in space. The dielectric constant of the insulator between the conductors determines the Velocity Factor per this formula: 1 over the square root of the dielectric constant. Lines using polyethylene have a Velocity Factor of 66%, foam polyethylene brings it above 80%. Actual Velocity Factor can vary by as much as plus or minus 10%. Because of that delay in propagation, a given physical length will always seem longer electrically.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Key words: IS NOT. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. In free space, waves are known as transverse-electromagnetic: the electric field, the magnetic field and the direction of travel are all perpendicular to one another. In a waveguide, waves bounce from wall to wall thus travelling in a zigzag manner. Only one of the electric or magnetic field can be truly perpendicular with the length of the waveguide; the mode, transverse electric or transverse magnetic, describes which field is purely perpendicular.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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A Microstrip transmission line is a type of line consisting of a thin and flat strip of conductive material separated from a ground plane by a dielectric. A double-sided printed circuit board lends itself to the construction of microstrip lines: traces on top with a ground plane underneath. Characteristic Impedance is determined by trace width, dielectric thickness and dielectric constant. One side of the line is exposed to air, external shielding may be required when high isolation is required. Stripline uses a similar thin and flat conductor but sandwiched between two parallel ground planes.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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A Microstrip transmission line is a type of line consisting of a thin and flat strip of conductive material separated from a ground plane by a dielectric. A double-sided printed circuit board lends itself to the construction of microstrip lines: traces on top with a ground plane underneath. Characteristic Impedance is determined by trace width, dielectric thickness and dielectric constant. One side of the line is exposed to air, external shielding may be required when high isolation is required. Stripline uses a similar thin and flat conductor but sandwiched between two parallel ground planes.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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Waveguides, used as transmission lines, are hollow pipes through which signals propagate as waves. The width or diameter of the waveguide must be slightly larger than a half-wavelength at the operating frequency. Below one gigahertz, dimensions become prohibitive. Signals with wavelengths too large for the physical size of the waveguide are attenuated: waveguides behave like high-pass filters, in other words, attenuation below the cutoff frequency. Waveguides do not suffer the conduction, dielectric or radiation losses that normal transmission lines present at microwave frequencies.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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A Microstrip transmission line is a type of line consisting of a thin and flat strip of conductive material separated from a ground plane by a dielectric. A double-sided printed circuit board lends itself to the construction of microstrip lines: traces on top with a ground plane underneath. Characteristic Impedance is determined by trace width, dielectric thickness and dielectric constant. External shielding may be required when high isolation is required. Stripline uses a similar thin and flat conductor but sandwiched between two parallel ground planes.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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With the possibility of shorter wavelengths to reach deeper into the body or to produce resonances in smaller structures, such as the eye, be extra careful not to expose anyone to microwave radiation. The significant gain available from physically small antennas also turn low power levels into definite risks. Heating is one known effect of RF on body tissues, other effects are possible.

Original copyright; explanations transcribed with permission from Francois VE2AAY, author of the ExHAMiner exam simulator. Do not copy without his permission.

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