KB6NU's Ham Radio Blog

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From the engineering magazines: scope measurements, op-amp BW,
travelling-wave tubes

Posted: 13 Jan 2016 09:07 AM PST
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Make great oscilloscope measurements.Â*In oscilloscopes today, making a good
signal measurement is easy. However, making a great measurement takes some
expertise.
Op amp basics: Small signal bandwidth and overall performance.Â*It is rare
to find an op amp data sheet without a bandwidth number on the front page.
Because small signal bandwidth is the largest number, this is usually the
number featured most prominently. A good question, though, is how important
is this number and how does it relate to other device performance metrics?

The quest for the ultimate vacuum tube.Â*In July 1962, the Telstar 1
satellitetook an enormous leap toward the globally connected world we now
take for granted. It relayed from space, for the first time ever, live
television images and telephone calls between continents: specifically, a
ground station in Andover, Maine, and other stations in England and France.
It accomplished this feat thanks to a microwave repeater that had at its
heart a slight but powerful vacuum device known as a traveling-wave tube.
The 30-centimeter-long,glass-walled electron tube was at the time the only
device capable of boosting a broadband television signal with enough power
to cross an ocean. Solid-state devices just weren’t up to the task.Â*More
than a half century later, traveling-wave-tube amplifiers stillÂ*dominate
satellite communication. That’s right—yourÂ*ultrahigh-definition satellite
TV and satellite radio come to you courtesy of vacuum tubes in space.



The post From the engineering magazines: scope measurements, op-amp BW,
travelling-wave tubes appeared first on KB6NUs Ham Radio Blog.


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2016 Extra Class Study Guide: E5B - Time constants, phase relationships,
admittance, susceptance

Posted: 12 Jan 2016 12:08 PM PST
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E5B Time constants and phase relationships: RLC time constants;
definition; time constants in RL and RC circuits; phase angle between
voltage and current; phase angles of series RLC; phase angle of inductance
vs susceptance; admittance and susceptance

When you put a voltage across a capacitor, current will flow into the
capacitor and the voltage across the capacitor will increase until the
voltage across it reaches the value of the supply voltage. This is not a
linear function. By that I mean that the voltage will increase quite
rapidly at first, but the rate of increase will slow as time goes on.

To see how this works, let’s consider the RC time constant. The time
constant of an RC circuit is equal to the resistance in the circuit times
the capacitance, or simply R x C. For example, the time constant of a
circuit having two 220-microfarad capacitors and two 1-megohm resistors,
all in parallel is 220 seconds. (E5B04)

The equivalent resistance of two 1 MΩ resistors in parallel is 500 kΩ. The
equivalent capacitance of two 220 μF capacitors in parallel is 440 μF. The
time constant is RxC = 440 x 10-6 x 500 x 103 = 220 s.

One time constant is the term for the time required for the capacitor in an
RC circuit to be charged to 63.2% of the applied voltage. (E5B01)
Similarly, one time constant is the term for the time it takes for a
charged capacitor in an RC circuit to discharge to 36.8% of its initial
voltage. (E5B02)

A capacitor charges to 86.5% of the applied voltage, or discharges to 13.5%
of the starting voltgage, after two time constants. After three time
constants, a capacitor is charged up to 95% of the applied voltage or
discharged to 5% of the starting voltage.
Phase relationships

In an AC circuit, with only resistors, the voltage and current are in
phase. What that means is that the voltage and current change in lock step.
When the voltage increases, the current increases. When the voltage
decreases, the current decreases.

When there are capacitors and inductors in an AC circuit, however, the
phase relationship between the voltage and current changes. Specifically,
the relationship between the current through a capacitor and the voltage
across a capacitor is that the current leads voltage by 90 degrees. (E5B09)
We could also say that the voltage lags the current by 90 degrees. See
figure below.

What that means is that the current through a capacitor increases and
decreases before the voltage across a capacitor increases and decreases. We
say that the current leads the voltage by 90 degrees because it starts
increasing one-quarter of a cycle before the voltage starts increasing.
The current leads the current in an AC circuit with a capacitive reactance.

The relationship between the current through an inductor and the voltage
across an inductor is that the voltage leads current by 90 degrees. (E5B10)
We could also say that the current lags the voltage. See figure below.

What that means is that the voltage across an inductor increases and
decreases before the current through the inductor increases and decreases.
We say that the voltage leads the voltage by 90 degrees because it starts
increasing one-quarter of a cycle before the current starts increasing.
The voltage leads the current in a circuit with inductive reactance.

When there are resistors as well as a capacitor or inductor or both in a
circuit, the relationship is a little more complicated. Let’s look at what
happens in the series RLC circuit shown below.
A series RLC circuit contains an inductive reactance, a capacitive
reactance, and a resistance all in series.

In this circuit, there is resistance, capacitive reactance, and inductive
reactance. The reactances subtract from one another. If the capacitive
reactance is greater than the inductive reactance, the net reactance will
be capacitive. If the inductive reactance is greater than the capacitive
reactance, the net reactance will be inductive.

The resistance and the reactance add to one another, but they add
vectorially. The reason for this is that the reactance will be 90 degrees
out of phase with the resistance. This is shown in the figure below.
Resistance and reactance add vectorially.

The magnitude of the impedance, Z, will be equal to √(R2 + X2) and the
tangent of the phase angle will be equal to X/R. Let’s see how this works
in several examples.

If XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms, the phase angle
between the voltage across and the current through the series RLC circuit
is 14.0 degrees with the voltage lagging the current. (E5B07) Here’s how to
calculate that:
X = XC XL = 250 Ω (capacitive)
phase angle = tan-1 (250/1000) = 14 degrees.

and because the reactance is capacitive, the voltage will lag the current.

If XC is 100 ohms, R is 100 ohms, and XL is 75 ohms, the phase angle
between the voltage across and the current through the series RLC circuit
is 14 degrees with the voltage lagging the current. (E5B08) Here’s the
calculation:
X = XC XL = 25 Ω (capacitive)
phase angle = tan-1 (25/100) = 14 degrees.

and because the reactance is capacitive, the voltage lags the current.

If XC is 25 ohms, R is 100 ohms, and XL is 50 ohms, the phase angle between
the voltage across and the current through the series RLC circuit is 14
degrees with the voltage leading the current. (E5B11) Here’s the
calculation:
X = XL XC = 25 Ω (inductive)
phase angle = tan-1 (25/100) = 14 degrees.

and because the reactance is inductive, the voltage leads the current.
Susceptance and admittance

While we most often work with reactances and impedances in amateur radio,
in some cases, its more advantageous to work with susceptance and
admittance.

Susceptance is the inverse of reactance.(E5B06) The unit of susceptance is
the mho. B is the letter is commonly used to represent susceptance. (E5B13)
In mathematical terms,
B = 1/X

When the magnitude of a reactance is converted to a susceptance, the
magnitude of the susceptance is the reciprocal of the magnitude of the
reactance. (E5B05) When the phase angle of a reactance is converted to a
susceptance, the sign is reversed. (E5B03)

Admittance is the inverse of impedance. (E5B12) The unit of admittance is
the Siemens, and like impedance, is a complex quantity.



The post 2016 Extra Class Study Guide: E5B – Time constants, phase
relationships, admittance, susceptance appeared first on KB6NUs Ham Radio
Blog.