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Subelement L02
Inductors and Capacitors.
Section L02
What is the meaning of the term "time constant" in an RL circuit?
  • The time required for the current in the circuit to build up to 36.8% of the maximum value
  • The time required for the voltage in the circuit to build up to 63.2% of the maximum value
  • The time required for the voltage in the circuit to build up to 36.8% of the maximum value
  • The time required for the current in the circuit to build up to 63.2% of the maximum value

Inductance is a property of circuits that oppose changes in current. The time constant is the time current WOULD need to reach final value IF the initial rate of change COULD be maintained. The time constant in seconds equals L in henrys divided by R in ohms: the lower the resistance, the greater the rate of change resulting in greater opposition. The current after 1, 2 and 5 time constants is respectively 63%, 87% and 100% of the final value. With capacitors, the ratios are the same but they relate to voltage; the time constant then becomes R times C.

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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What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the supply voltage?
  • An exponential rate of one
  • A time factor of one
  • One exponential period
  • One time constant

Capacitance is a property of circuits that oppose changes in voltage. Under charging conditions, the time constant is the time voltage WOULD need to reach the final value IF the initial rate of change COULD be maintained. The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. The voltage after 1, 2 and 5 times constants is respectively 63%, 87% and 100% of the final value. With inductors, the ratios are the same but they relate to current; the time constant then becomes L divided by R.

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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What is the term for the time required for the current in an RL circuit to build up to 63.2% of the maximum value?
  • One time constant
  • An exponential period of one
  • A time factor of one
  • One exponential rate

Inductance is a property of circuits that oppose changes in current. The time constant is the time current WOULD need to reach final value IF the initial rate of change COULD be maintained. The time constant in seconds equals L in henrys divided by R in ohms: the lower the resistance, the greater the rate of change resulting in greater opposition. The current after 1, 2 and 5 time constants is respectively 63%, 87% and 100% of the final value. With capacitors, the ratios are the same but they relate to voltage; the time constant then becomes R times C.

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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What is the term for the time it takes for a charged capacitor in an RC circuit to discharge to 36.8% of its initial value of stored charge?
  • One time constant
  • A discharge factor of one
  • An exponential discharge of one
  • One discharge period

Key word: DISCHARGE. The time constant is the time voltage WOULD need to reach the final value IF the initial rate of change COULD be maintained. The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. The voltage after 1, 2 and 5 times constants is respectively 63%, 87% and 100% of the final value. Heading towards ZERO, we are left with 37% (100 minus 63) and 13% (100 minus 87) respectively after 1 and 2 time constants.

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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What is meant by "back EMF"?
  • A voltage that opposes the applied EMF
  • A current that opposes the applied EMF
  • An opposing EMF equal to R times C percent of the applied EMF
  • A current equal to the applied EMF

'Back EMF' or 'counter electromotive force' is the voltage induced by changing current in an inductor. It is the force opposing changes in current through inductors.

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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After two time constants, the capacitor in an RC circuit is charged to what percentage of the supply voltage?
  • 86.5%
  • 63.2%
  • 95%
  • 36.8%

Capacitance is a property of circuits that oppose changes in voltage. Under charging conditions, the time constant is the time voltage WOULD need to reach the final value IF the initial rate of change COULD be maintained. The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. The voltage after 1, 2 and 5 times constants is respectively 63%, 87% and 100% of the final value. With inductors, the ratios are the same but they relate to current; the time constant then becomes L divided by R.

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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After two time constants, the capacitor in an RC circuit is discharged to what percentage of the starting voltage?
  • 13.5%
  • 36.8%
  • 86.5%
  • 63.2%

Key word: DISCHARGE. The time constant is the time voltage WOULD need to reach the final value IF the initial rate of change COULD be maintained. The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. The voltage after 1, 2 and 5 times constants is respectively 63%, 87% and 100% of the final value. Heading towards ZERO, we are left with 37% (100 minus 63) and 13% (100 minus 87) respectively after 1 and 2 time constants.

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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What is the time constant of a circuit having a 100 microfarad capacitor in series with a 470 kilohm resistor?
  • 470 seconds
  • 0.47 seconds
  • 47 seconds
  • 4700 seconds

The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. In multiplying microfarads and megohms, the prefixes cancel one another. 100 microfarads times 0.470 megohm = 100 times 0.47 = 47 seconds.

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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What is the time constant of a circuit having a 470 microfarad capacitor in series with a 470 kilohm resistor?
  • 47 000 seconds
  • 470 seconds
  • 221 seconds
  • 221 000 seconds

The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. In multiplying microfarads and megohms, the prefixes cancel one another. 470 microfarads times 0.470 megohm = 470 times 0.47 = 221 seconds.

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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What is the time constant of a circuit having a 220 microfarad capacitor in series with a 470 kilohm resistor?
  • 470 seconds
  • 220 seconds
  • 103 seconds
  • 470 000 seconds

The time constant in seconds equals R in ohms times C in farads: the higher the resistance, the longer the time. In multiplying microfarads and megohms, the prefixes cancel one another. 220 microfarads times 0.470 megohm = 220 times 0.47 = 103 seconds.

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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What is the result of skin effect?
  • Thermal effects on the surface of the conductor increase impedance
  • Thermal effects on the surface of the conductor decrease impedance
  • As frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface
  • As frequency decreases, RF current flows in a thinner layer of the conductor, closer to the surface

Skin Effect is the tendency of AC to flow in an increasingly thinner layer at the surface of a conductor as frequency increases.

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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What effect causes most of an RF current to flow along the surface of a conductor?
  • Resonance effect
  • Layer effect
  • Skin effect
  • Piezoelectric effect

Skin Effect is the tendency of AC to flow in an increasingly thinner layer at the surface of a conductor as frequency increases.

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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Where does almost all RF current flow in a conductor?
  • In a magnetic field in the centre of the conductor
  • In a magnetic field around the conductor
  • In the centre of the conductor
  • Along the surface of the conductor

Skin Effect is the tendency of AC to flow in an increasingly thinner layer at the surface of a conductor as frequency increases.

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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Why does most of an RF current flow within a very thin layer under the conductor's surface?
  • Because of heating of the conductor's interior
  • Because of skin effect
  • Because the RF resistance of a conductor is much less than the DC resistance
  • Because a conductor has AC resistance due to self-inductance

Skin Effect is the tendency of AC to flow in an increasingly thinner layer at the surface of a conductor as frequency increases.

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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Why is the resistance of a conductor different for RF currents than for direct currents?
  • Because of the Hertzberg effect
  • Because conductors are non-linear devices
  • Because the insulation conducts current at high frequencies
  • Because of skin effect

Skin Effect is the tendency of AC to flow in an increasingly thinner layer at the surface of a conductor as frequency increases.

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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What unit measures the ability of a capacitor to store electrical charge?
  • Coulomb
  • Watt
  • Volt
  • Farad

Capacitors store energy in an electrostatic field. The capacitance in farads is one factor influencing how much energy can be stored in a capacitor. The coulomb is a quantity of electrons ( 6 times 10 exponent 18 ). One farad accepts a charge of one coulomb when subjected to one volt. The watt is a rate of doing work (one joule per second). One volt, a force, moves one coulomb with one joule of energy.

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 wire has a current passing through it. Surrounding this wire there is:
  • an electromagnetic field
  • an electrostatic field
  • a cloud of electrons
  • a skin effect that diminishes with distance

An electromagnetic field is the magnetic field created around a conductor carrying current. A magnetic field is a space around a magnet or a conductor where a magnetic force is present. A magnetic field is composed of magnetic lines of force. An electrostatic field is the electric field present between objects with different static electrical charges. An electric field is a space where an electrical charge exerts a force (attraction or repulsion) on other charges.

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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In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow?
  • In the same direction as the current
  • In the direct opposite to the current
  • In the direction determined by the left-hand rule
  • In all directions

The 'Left-hand Rule': position the left hand with your thumb pointing in the direction of electron flow; encircle the conductor with the remaining fingers, the fingers point in the direction of the magnetic lines of force. [ Using conventional current flow, this would become the Right-hand rule. ]

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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What is the term for energy that is stored in an electromagnetic or electrostatic field?
  • Potential energy
  • Kinetic energy
  • Ampere-joules
  • Joule-coulombs

Key word: STORED. Potential: "capable of coming into being or action (Canadian Oxford)". Kinetic: "of or due to motion (Canadian Oxford)".

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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Between the charged plates of a capacitor there is:
  • an electrostatic field
  • a magnetic field
  • a cloud of electrons
  • an electric current

Voltage across a capacitor creates an electrostatic field between the plates. An electrostatic field is the electric field present between objects with different static electrical charges. An electric field is a space where an electrical charge exerts a force (attraction or repulsion) on other charges.

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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Energy is stored within an inductor that is carrying a current. The amount of energy depends on this current, but it also depends on a property of the inductor. This property has the following unit:
  • watt
  • henry
  • coulomb
  • farad

Inductors store energy in an electromagnetic field. The inductance in henrys is one factor influencing how much energy can be stored in an inductor. One henry produces one volt of counter EMF with current changing at a rate of one ampere per second. The coulomb is a quantity of electrons ( 6 times 10 exponent 18 ). One farad accepts a charge of one coulomb when subjected to one volt. The watt is a rate of doing work (one joule per second).

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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What is the resonant frequency of a series RLC circuit if R is 47 ohms, L is 50 microhenrys and C is 40 picofarads?
  • 1.78 MHz
  • 7.96 MHz
  • 79.6 MHz
  • 3.56 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 50 times 40 equals 2000 ; The square root of 2000 is 44.7 ; 44.7 times 2 times 3.14 is 280.7 ; 1000 divided by 280.7 is 3.56 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 40 microhenrys and C is 200 picofarads?
  • 1.99 kHz
  • 1.99 MHz
  • 1.78 kHz
  • 1.78 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 40 times 200 equals 8000 ; The square root of 8000 is 89.4 ; 89.4 times 2 times 3.14 is 561.4 ; 1000 divided by 561.4 is 1.78 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 50 microhenrys and C is 10 picofarads?
  • 3.18 MHz
  • 3.18 kHz
  • 7.12 MHz
  • 7.12 kHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 50 times 10 equals 500 ; The square root of 500 is 22.4 ; 22.4 times 2 times 3.14 is 140.7 ; 1000 divided by 140.7 is 7.11 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 25 microhenrys and C is 10 picofarads?
  • 63.7 MHz
  • 10.1 kHz
  • 63.7 kHz
  • 10.1 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 25 times 10 equals 250 ; The square root of 250 is 15.8 ; 15.8 times 2 times 3.14 is 99.2 ; 1000 divided by 99.2 is 10.08 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 3 microhenrys and C is 40 picofarads?
  • 13.1 MHz
  • 13.1 kHz
  • 14.5 kHz
  • 14.5 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 3 times 40 equals 120 ; The square root of 120 is 11 ; 11 times 2 times 3.14 is 69.1 ; 1000 divided by 69.1 is 14.47 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 4 microhenrys and C is 20 picofarads?
  • 19.9 MHz
  • 19.9 kHz
  • 17.8 kHz
  • 17.8 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 4 times 20 equals 80 ; The square root of 80 is 8.9 ; 8.9 times 2 times 3.14 is 55.9 ; 1000 divided by 55.9 is 17.89 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 8 microhenrys and C is 7 picofarads?
  • 2.13 MHz
  • 21.3 MHz
  • 28.4 MHz
  • 2.84 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 8 times 7 equals 56 ; The square root of 56 is 7.5 ; 7.5 times 2 times 3.14 is 47.1 ; 1000 divided by 47.1 is 21.23 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 3 microhenrys and C is 15 picofarads?
  • 23.7 kHz
  • 23.7 MHz
  • 35.4 MHz
  • 35.4 kHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 3 times 15 equals 45 ; The square root of 45 is 6.7 ; 6.7 times 2 times 3.14 is 42.1 ; 1000 divided by 42.1 is 23.75 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 4 microhenrys and C is 8 picofarads?
  • 28.1 MHz
  • 49.7 MHz
  • 49.7 kHz
  • 28.1 kHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 4 times 8 equals 32 ; The square root of 32 is 5.7 ; 5.7 times 2 times 3.14 is 35.8 ; 1000 divided by 35.8 is 27.93 MHz.

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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What is the resonant frequency of a series RLC circuit, if R is 47 ohms, L is 1 microhenry and C is 9 picofarads?
  • 53.1 MHz
  • 5.31 MHz
  • 17.7 MHz
  • 1.77 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 1 times 9 equals 9 ; The square root of 9 is 3 ; 3 times 2 times 3.14 is 18.8 ; 1000 divided by 18.8 is 53.19 MHz.

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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What is the value of capacitance (C) in a series R-L-C circuit, if the circuit resonant frequency is 14.25 MHz and L is 2.84 microhenrys?
  • 44 microfarads
  • 2.2 picofarads
  • 44 picofarads
  • 2.2 microfarads

Method A: Reactances are equal at resonance. XL = 2 times 3.14 times 14.25 times 2.84 = 254.2 ohms. XC = 1 over ( 2 pi f C ). Restating for f in megahertz and C in picofarads, XC = one million over 2 pi megahertz times picofarads. Thus, C = one million over ( 2 pi f XC ) ; 2 times 3.14 times 14.25 times 254.2 = 22 748 ; one million divided by 22 748 = 43.96 picofarads. Method B: at 14 MHz, C has to be in picofarads; test the two answers in picofarads with "resonant frequency in megahertz equals 1000 over ( 2 pi times the square root of microhenrys times picofarads )".

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 1 microhenry and C is 10 picofarads?
  • 50.3 MHz
  • 15.9 kHz
  • 50.3 kHz
  • 15.9 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 1 times 10 equals 10 ; The square root of 9 is 3.2 ; 3.2 times 2 times 3.14 is 20.1 ; 1000 divided by 20.1 is 49.75 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 2 microhenrys and C is 15 picofarads?
  • 29.1 kHz
  • 5.31 MHz
  • 5.31 kHz
  • 29.1 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 2 times 15 equals 30 ; The square root of 30 is 5.5 ; 5.5 times 2 times 3.14 is 34.5 ; 1000 divided by 34.5 is 28.99 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 5 microhenrys and C is 9 picofarads?
  • 3.54 kHz
  • 23.7 MHz
  • 23.7 kHz
  • 3.54 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 5 times 9 equals 45 ; The square root of 45 is 6.7 ; 6.7 times 2 times 3.14 is 42.1 ; 1000 divided by 42.1 is 23.75 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 2 microhenrys and C is 30 picofarads?
  • 20.5 MHz
  • 2.65 MHz
  • 2.65 kHz
  • 20.5 kHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 2 times 30 equals 60 ; The square root of 60 is 7.7 ; 7.7 times 2 times 3.14 is 48.4 ; 1000 divided by 48.4 is 20.66 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 15 microhenrys and C is 5 picofarads?
  • 18.4 kHz
  • 18.4 MHz
  • 2.12 kHz
  • 2.12 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 15 times 5 equals 75 ; The square root of 75 is 8.7 ; 8.7 times 2 times 3.14 is 54.6 ; 1000 divided by 54.6 is 18.32 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 3 microhenrys and C is 40 picofarads?
  • 1.33 kHz
  • 1.33 MHz
  • 14.5 kHz
  • 14.5 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 3 times 40 equals 120 ; The square root of 120 is 11 ; 11 times 2 times 3.14 is 69.1 ; 1000 divided by 69.1 is 14.47 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 40 microhenrys and C is 6 picofarads?
  • 6.63 MHz
  • 6.63 kHz
  • 10.3 kHz
  • 10.3 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 40 times 6 equals 240 ; The square root of 240 is 15.5 ; 15.5 times 2 times 3.14 is 97.3 ; 1000 divided by 97.3 is 10.28 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 10 microhenrys and C is 50 picofarads?
  • 7.12 kHz
  • 3.18 MHz
  • 3.18 kHz
  • 7.12 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 10 times 50 equals 500 ; The square root of 500 is 22.4 ; 22.4 times 2 times 3.14 is 140.7 ; 1000 divided by 140.7 is 7.11 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 200 microhenrys and C is 10 picofarads?
  • 7.96 kHz
  • 3.56 MHz
  • 3.56 kHz
  • 7.96 MHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 200 times 10 equals 2000 ; The square root of 2000 is 44.7 ; 44.7 times 2 times 3.14 is 280.7 ; 1000 divided by 280.7 is 3.56 MHz.

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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What is the resonant frequency of a parallel RLC circuit if R is 4.7 kilohms, L is 90 microhenrys and C is 100 picofarads?
  • 1.68 MHz
  • 1.77 kHz
  • 1.77 MHz
  • 1.68 kHz

Resonant frequency equals 1 over ( 2 pi times the square root of L times C ). Restating for frequency in megahertz becomes 1000 over ( 2 pi times the square root of microhenrys times picofarads ). 90 times 100 equals 9000 ; The square root of 9000 is 94.9 ; 94.9 times 2 times 3.14 is 596 ; 1000 divided by 596 is 1.68 MHz.

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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What is the value of inductance (L) in a parallel RLC circuit, if the resonant frequency is 14.25 MHz and C is 44 picofarads?
  • 0.353 microhenry
  • 2.8 microhenrys
  • 253.8 millihenrys
  • 3.9 millihenrys

Method A: Reactances are equal at resonance. XC = 1 over ( 2 pi f C ). Restating for f in megahertz and C in picofarads, XC = one million over (2 pi times megahertz times picofarads). XC = one million divided by ( 2 times 3.14 times 14.25 times 44 ) = 254 ohms. With XL = 2 pi f L, L is XL divided by 2 pi f: 254 divided by ( 2 times 3.14 times 14.25 ) = 2.8 microhenrys. Method B: at 14 MHz, L has to be in microhenrys; test the two answers in microhenrys with "resonant frequency in megahertz equals 1000 over ( 2 pi times the square root of microhenrys times picofarads )".

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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What is the Q of a parallel RLC circuit, if it is resonant at 14.128 MHz, L is 2.7 microhenrys and R is 18 kilohms?
  • 75.1
  • 7.51
  • 0.013
  • 71.5

Reactance = 2 pi f L = 2 times 3.14 times 14.128 times 2.7 = 240 ( the mega in megahertz cancels the micro in microhenrys). Q = 18 000 divided by 240 = 75 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 14.128 MHz, L is 4.7 microhenrys and R is 18 kilohms?
  • 43.1
  • 13.3
  • 0.023
  • 4.31

Reactance = 2 pi f L = 2 times 3.14 times 14.128 times 4.7 = 417 ( the mega in megahertz cancels the micro in microhenrys). Q = 18 000 divided by 417 = 43 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 4.468 MHz, L is 47 microhenrys and R is 180 ohms?
  • 0.136
  • 7.35
  • 0.00735
  • 13.3

Reactance = 2 pi f L = 2 times 3.14 times 4.468 times 47 = 1319 ( the mega in megahertz cancels the micro in microhenrys). Q = 180 divided by 1319 = 0.136 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 14.225 MHz, L is 3.5 microhenrys and R is 10 kilohms?
  • 71.5
  • 31.9
  • 7.35
  • 0.0319

Reactance = 2 pi f L = 2 times 3.14 times 14.225 times 3.5 = 313 ( the mega in megahertz cancels the micro in microhenrys). Q = 10 000 divided by 313 = 31.9 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 7.125 MHz, L is 8.2 microhenrys and R is 1 kilohm?
  • 2.73
  • 36.8
  • 0.368
  • 0.273

Reactance = 2 pi f L = 2 times 3.14 times 7.125 times 8.2 = 367 ( the mega in megahertz cancels the micro in microhenrys). Q = 1000 divided by 367 = 2.7 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 7.125 MHz, L is 10.1 microhenrys and R is 100 ohms?
  • 0.00452
  • 4.52
  • 0.221
  • 22.1

Reactance = 2 pi f L = 2 times 3.14 times 7.125 times 10.1 = 452 ( the mega in megahertz cancels the micro in microhenrys). Q = 100 divided by 452 = 0.22 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 7.125 MHz, L is 12.6 microhenrys and R is 22 kilohms?
  • 22.1
  • 0.0256
  • 25.6
  • 39

Reactance = 2 pi f L = 2 times 3.14 times 7.125 times 12.6 = 564 ( the mega in megahertz cancels the micro in microhenrys). Q = 22 000 divided by 564 = 39 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 3.625 MHz, L is 3 microhenrys and R is 2.2 kilohms?
  • 25.6
  • 31.1
  • 0.031
  • 32.2

Reactance = 2 pi f L = 2 times 3.14 times 3.625 times 3 = 68 ( the mega in megahertz cancels the micro in microhenrys). Q = 2200 divided by 68 = 32.3 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 3.625 MHz, L is 42 microhenrys and R is 220 ohms?
  • 0.00435
  • 0.23
  • 2.3
  • 4.35

Reactance = 2 pi f L = 2 times 3.14 times 3.625 times 42 = 956 ( the mega in megahertz cancels the micro in microhenrys). Q = 220 divided by 956 = 0.23 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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What is the Q of a parallel RLC circuit, if it is resonant at 3.625 MHz, L is 43 microhenrys and R is 1.8 kilohms?
  • 0.543
  • 54.3
  • 23
  • 1.84

Reactance = 2 pi f L = 2 times 3.14 times 3.625 times 43 = 979 ( the mega in megahertz cancels the micro in microhenrys). Q = 1800 divided by 979 = 1.84 . In a PARALLEL circuit loaded by a resistor, Q = Resistance divided by Reactance: the higher the parallel resistance, the lesser the effect on the response curve. Parallel resistance lowers the Q of a parallel tuned circuit. A parallel Damping Resistor is used to increase bandwidth.

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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Why is a resistor often included in a parallel resonant circuit?
  • To increase the Q and decrease bandwidth
  • To decrease the Q and increase the bandwidth
  • To increase the Q and decrease the skin effect
  • To decrease the Q and increase the resonant frequency

A Damping Resistor can be placed across a parallel resonant circuit, or in series with a series resonant circuit, to lower the Q. Reducing the Quality factor increases bandwidth.

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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What is a crystal lattice filter?
  • A filter with narrow bandwidth and steep skirts made using quartz crystals
  • A filter with wide bandwidth and shallow skirts made using quartz crystals
  • An audio filter made with four quartz crystals that resonate at 1 kHz intervals
  • A power supply filter made with interlaced quartz crystals

A filter with narrow bandwidth and steep skirts made with quartz crystals. "Lattice: a structure of crossed laths with spaces between, used as a screen or fence." The frequency separation between the crystals sets the bandwidth and the response shape. Crystal lattice filter: uses two matched pairs of series crystals and a higher-frequency matched pair of shunt crystals in a balanced configuration. Half-lattice crystal filter: uses two crystals in an unbalanced configuration. Such filters can be cascaded. A 'Crystal Gate' uses a single crystal.

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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What factor determines the bandwidth and response shape of a crystal lattice filter?
  • The gain of the RF stage following the filter
  • The amplitude of the signals passing through the filter
  • The relative frequencies of the individual crystals
  • The centre frequency chosen for the filter

A filter with narrow bandwidth and steep skirts made with quartz crystals. "Lattice: a structure of crossed laths with spaces between, used as a screen or fence." The frequency separation between the crystals sets the bandwidth and the response shape. Crystal lattice filter: uses two matched pairs of series crystals and a higher-frequency matched pair of shunt crystals in a balanced configuration. Half-lattice crystal filter: uses two crystals in an unbalanced configuration. Such filters can be cascaded. A 'Crystal Gate' uses a single crystal.

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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For single-sideband phone emissions, what would be the bandwidth of a good crystal lattice filter?
  • 2.4 kHz
  • 15 kHz
  • 500 Hz
  • 6 kHz

Speech frequencies on a communication-grade SSB voice channel range from 300 hertz to 3000 hertz and thus require a bandwidth of 2.7 kHz; 2.1 kHz is a good compromise between fidelity and selectivity. 15 kHz is the bandwidth of FM, 6 kHz is for AM, 500 Hz is a common filter width for CW.

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A quartz crystal filter is superior to an LC filter for narrow bandpass applications because of the:
  • LC circuit's high Q
  • crystal's simplicity
  • crystal's high Q
  • crystal's low Q

Piezoelectric crystals behave like tuned circuits with an extremely high "Q" ("Quality Factor", in excess of 25 000). Their accuracy and stability are outstanding.

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Piezoelectricity is generated by:
  • touching crystals with magnets
  • adding impurities to a crystal
  • moving a magnet near a crystal
  • deforming certain crystals

The piezoelectric property of quartz is two-fold: apply mechanical stress to a crystal and it produces a small electrical field; subject quartz to an electrical field and the crystal changes dimensions slightly. Crystals are capable of resonance either at a fundamental frequency depending on their physical dimensions or at overtone frequencies near odd-integer multiples (3rd, 5th, 7th, etc.). Piezoelectric crystals can serve as filters because of their extremely high "Q" (> 25 000) or as stable, noise-free and accurate frequency references.

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Electrically, what does a crystal look like?
  • A variable tuned circuit
  • A very high Q tuned circuit
  • A very low Q tuned circuit
  • A variable capacitance

Piezoelectric crystals behave like tuned circuits with an extremely high "Q" ("Quality Factor", in excess of 25 000). Their accuracy and stability are outstanding.

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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Crystal oscillators, filters and microphones depend upon which principle?
  • Hertzberg effect
  • Ferro-resonance
  • Overtone effect
  • Piezoelectric effect

The piezoelectric property of quartz (generating electricity under mechanical stress, bending when subjected to electric field) is used in crystal-based oscillators, radio-frequency crystal filters, such as the lattice filter, and crystal microphones. The Active Filter is based on an active device, generally an operational amplifier, and a network of resistors and capacitors.

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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Crystals are not applicable to which of the following?
  • Lattice filters
  • Oscillators
  • Active filters
  • Microphones

The piezoelectric property of quartz (generating electricity under mechanical stress, bending when subjected to electric field) is used in crystal-based oscillators, radio-frequency crystal filters, such as the lattice filter, and crystal microphones. The Active Filter is based on an active device, generally an operational amplifier, and a network of resistors and capacitors.

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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What are the three general groupings of filters?
  • Hartley, Colpitts and Pierce
  • Audio, radio and capacitive
  • Inductive, capacitive and resistive
  • High-pass, low-pass and band-pass

There are 4 categories of filters: high-pass, low-pass, band-pass and band-stop. Hartley, Colpitts and Pierce are oscillator configurations. "Capacitive" is not a range of frequencies like audio or radio. Resistors do not discriminate frequency.

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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What are the distinguishing features of a Butterworth filter?
  • It only requires conductors
  • It only requires capacitors
  • It has a maximally flat response over its pass-band
  • The product of its series and shunt-element impedances is a constant for all frequencies

The Butterworth class of filters exhibit "maximally flat response": smooth response, no passband ripple. Their frequency response is as flat as mathematically possible in the passband, no bumps or variations (ripple) [first described by British engineer Stephen Butterworth]. The Chebyshev class of filters [in honour of Pafnuty Chebyshev, a Russian mathematician] have steeper cutoff slopes and more ripple than Butterworth filters. Elliptic filters are sharper than the previous two. Here is a mnemonic trick: "The Butterworth's response is smooth as butter".

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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Which filter type is described as having ripple in the passband and a sharp cutoff?
  • A Butterworth filter
  • A Chebyshev filter
  • An active LC filter
  • A passive op-amp filter

The Butterworth class of filters exhibit "maximally flat response": smooth response, no passband ripple. Their frequency response is as flat as mathematically possible in the passband, no bumps or variations (ripple) [first described by British engineer Stephen Butterworth]. The Chebyshev class of filters [in honour of Pafnuty Chebyshev, a Russian mathematician] have steeper cutoff slopes and more ripple than Butterworth filters. Elliptic filters are sharper than the previous two. Here is a mnemonic trick: "The Butterworth's response is smooth as butter".

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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What are the distinguishing features of a Chebyshev filter?
  • It has a maximally flat response in the passband
  • It allows ripple in the passband in return for steeper skirts
  • It requires only inductors
  • It requires only capacitors

The Butterworth class of filters exhibit "maximally flat response": smooth response, no passband ripple. Their frequency response is as flat as mathematically possible in the passband, no bumps or variations (ripple) [first described by British engineer Stephen Butterworth]. The Chebyshev class of filters [in honour of Pafnuty Chebyshev, a Russian mathematician] have steeper cutoff slopes and more ripple than Butterworth filters. Elliptic filters are sharper than the previous two. Here is a mnemonic trick: "The Butterworth's response is smooth as butter".

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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Resonant cavities are used by amateurs as a:
  • high-pass filter above 30 MHz
  • narrow bandpass filter at VHF and higher frequencies
  • power line filter
  • low-pass filter below 30 MHz

The quarter wavelength Resonant Cavity behaves like a very high "Q" filter. Due to their physical size, they become practical only at VHF frequencies: at 50 MHz (6 m), the length of the cavity is 1.5 m (one quarter wavelength).

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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On VHF and above, 1/4 wavelength coaxial cavities are used to give protection from high-level signals. For a frequency of approximately 50 MHz, the diameter of such a device would be about 10 cm (4 in). What would be its approximate length?
  • 0.6 metres (2 ft)
  • 2.4 metres (8 ft)
  • 3.7 metres (12 ft)
  • 1.5 metres (5 ft)

The quarter wavelength Resonant Cavity behaves like a very high "Q" filter (around 3000). Due to their physical size, they become practical only at VHF frequencies: at 50 MHz (6 m), the length of the cavity is 1.5 m (one quarter wavelength).

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 device which helps with receiver overload and spurious responses at VHF, UHF and above may be installed in the receiver front end. It is called a:
  • directional coupler
  • duplexer
  • helical resonator
  • diplexer

The Helical Resonator, based on the concept of a resonant helically-wound section of transmission line within a shielded enclosure, achieves selectivity comparable to the quarter-wave resonant cavity but with a substantial size reduction.

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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Where you require bandwidth at VHF and higher frequencies about equal to a television channel, a good choice of filter is the:
  • Butterworth
  • Chebyshev
  • none of the other answers
  • resonant cavity

The bandwidth of a fast-scan TV channel is 6 MHz; that is much too wide for any of the filters listed.

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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What is the primary advantage of the Butterworth filter over the Chebyshev filter?
  • It requires only capacitors
  • It has maximally flat response over its passband
  • It allows ripple in the passband in return for steeper skirts
  • It requires only inductors

The Butterworth class of filters exhibit "maximally flat response": smooth response, no passband ripple. Their frequency response is as flat as mathematically possible in the passband, no bumps or variations (ripple) [first described by British engineer Stephen Butterworth]. The Chebyshev class of filters [in honour of Pafnuty Chebyshev, a Russian mathematician] have steeper cutoff slopes and more ripple than Butterworth filters. Elliptic filters are sharper than the previous two. Here is a mnemonic trick: "The Butterworth's response is smooth as butter".

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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What is the primary advantage of the Chebyshev filter over the Butterworth filter?
  • It requires only inductors
  • It has maximally flat response over the passband
  • It allows ripple in the passband in return for steeper skirts
  • It requires only capacitors

The Butterworth class of filters exhibit "maximally flat response": smooth response, no passband ripple. Their frequency response is as flat as mathematically possible in the passband, no bumps or variations (ripple) [first described by British engineer Stephen Butterworth]. The Chebyshev class of filters [in honour of Pafnuty Chebyshev, a Russian mathematician] have steeper cutoff slopes and more ripple than Butterworth filters. Elliptic filters are sharper than the previous two. Here is a mnemonic trick: "The Butterworth's response is smooth as butter".

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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Which of the following filter types is not suitable for use at audio and low radio frequencies?
  • Elliptical
  • Chebyshev
  • Butterworth
  • Cavity

The quarter wavelength Resonant Cavity behaves like a very high "Q" filter. Due to their physical size, they become practical only at VHF frequencies: at 50 MHz (6 m), the length of the cavity is 1.5 m (one quarter wavelength).

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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