A frequency counter has an internal frequency reference it uses to compare against the signal being measured. "Time base" is another term for "frequency reference" (frequency being the reciprocal of time, therefore a time reference is also a frequency reference). The more accurate the time base, the more accurate the frequency counter.

The other 3 factors mentioned are insignificant -- an attenuator changes the amplitude of the signal but not the frequency; and the logic components (including a decade divider) have no cumulative effect on accuracy since they are referenced to the time base.

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\begin{align} \frac{\text{Ohms}}{\text{volt}} \times \text{full scale volts} &= \text{full scale impedance} \\ &=\text{input impedance} \end{align} (drichmond60)

Hint: all the "When used as..." answers are incorrect. (KG5KOU)

Hint: The word "voltmeter" appears in the question and in the correct answer.

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The 2-port S (scattering) voltage parameters for a linear electrical network are defined as

S₁₁ = input reflection coefficient
S₁₂ = reverse gain
S₂₁ = forward gain
S₂₂ = output reflection coefficient

Therefore, S₂₁ is the forward gain.

Hint: S_ab is the outgoing wave at Port a when there is an incoming wave at Port B and there is no incoming wave at the other port.

See https://en.wikipedia.org/wiki/Scattering_parameters for a summary of the technical explanation

Mnemonic:
21: Big element followed by a small element is a Yagi with forward gain
12: Small element followed by a big element is a Yagi pointing the other way giving reverse gain.
11: The 1 sees a reflection and 1 looks like I for input.
22: The 2 sees a reflection and 2 does not look like an I.

---

Poor man's hint: In the United States, you look forward to turning 21 years old.

Another stupid hint: the greater number of 2 in S21 is before (forward) the 1. The reverse is true with reverse gain (pun unintended).

One more stupid hint: Watch out, because there are two very similar questions like this. The way you can remember is this question is shorter, so choose the bigger number. The other question is longer, so choose the smaller number. If that makes sense.

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The 2-port \(S\) (scattering) voltage parameters for a linear electrical network are defined as

\[\begin{align} S_{11} &= \text{input reflection coefficient} \\ S_{12} &= \text{reverse gain} \\ S_{21} &= \text{forward gain} \\ S_{22} &= \text{output reflection coefficient} \\ \end{align}\]

SWR and signal return loss are both calculated by using the input reflection coefficient. Therefore, \(S_{11}\) represents return loss. SWR can be directly calculated from S11 by a simple formula.

See https://en.wikipedia.org/wiki/Scattering_parameters for a summary of the technical explanation

Silly memory tip: The straight lines of "11" look like the tips of an electrical plug you "input" into a electrical socket.

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\(50\Omega\) ohms is the most common impedance used in RF power systems, and amateur transmitters also use this standard. Therefore it is a useful point to calibrate to. After that, short-circuit and open-circuit are two "boundary cases" that ensure the analyzer behaves correctly at the edges of its range.

Calibrating to \(75\Omega\) or \(90\Omega\) ohms might be somewhat helpful, but after covering the full range with the 3 correct answers there is limited value in any further calibration. The other answers are not simple loads or make no sense at all.

Funny reminder: The movie "short circuit" and the robot Johnny 5. Only 1 answer has "short circuit" and 5 (\(50\Omega\)) in it.

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Where \(P\) is power:

\begin{align} \text{(load absorption)} &= P_\text{forward} - P_\text{reflected} &=100-25=75\:\text{Watts} \end{align}

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S parameters are a way of measuring the frequency response of devices and can refer to as many ports as are on the device.

For example, an antenna has 1 port, a filter may have 2 ports, a power divider may have 3 or more ports.

The subscripts tell us from which ports the measurements were made and are in the order of "To -> From" or S_<out><in>

So S₁₁ would be a measurement to Port 1, from Port 1. (Perhaps an antenna measurement, or other reflection measurement).

S₂₁ would be a measurement made at port 2 with the signal being delivered from port 1. (Such as measuring a filter to see what frequencies are blocked or passed through).

Silly hint: Submarines go to ports Silly hint: Think "Sports" as in football, basebasell, etc. for S Ports

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Quick silly attempt at remembering the right answer:

The right answer has "frequency response" in it. So, Every Question (Q) deserves a response

(you're welcome)

Q stands for quality. The frequency response is a measurement of quality.

Definition Of \(Q\) Factor: In the context of resonators, \(Q\) is defined in terms of the ratio of the energy stored in the resonator to the energy supplied by a generator, per cycle, to keep signal amplitude constant, at a frequency \(f_r\) (the resonant frequency), where the stored energy is constant with time:

\[\begin{align} Q &= 2π \times \left( \frac{\text{Energy}_{\text{stored}}}{\text{Energy}_{\text{dissipated per cycle}}} \right) \\ &= 2π\times f_r \times \left( \frac{\text{Energy}_{\text{stored}}}{\text{Power}_{\text{loss}}} \right) \end{align}\]

http://en.wikipedia.org/wiki/Q_factor#Explanation

There are a few ways to define \(Q\). With regard to this question, the bandwidth is the width of the range of frequencies for which the energy is at least half its peak value. The higher the \(Q\), the narrower the bandwidth. That is,

\[\text{bandwidth} = \frac{f_r}{Q}\]

-wileyj2956

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A simple elimination leads to the correct answer. We use audio to modulate the carrier in SSB mode so the answer saying use radio frequencies is clearly wrong.

The question is asking about measuring the resulting inter-modulated signal. A logic analyzer is clearly not applicable and a peak reading wattmeter is not used to measure distortion.

This leads us to the correct answer:

Modulate the transmitter with two non-harmonically related audio frequencies and observe the RF output with a spectrum analyzer

Still, read the answers slowly as it's very easy to mistakenly choose the answer that says radio and not audio (ericthughes)

Hint: only the correct answer contains both "audio" and "spectrum analyzer" (KG5KOU) The Answer shown in the example is missing the word "Audio" that is described in the hint. (KD8BXY)

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A Vector Network Analyzer is fundamentally a device for measuring incident and reflected power, usually expressed as S Parameters (Scattering Parameters).

While Input Impedance and Output Impedance are not actually S Parameters, these things can be calculated based on a combination of S parameter measurements and calibration data. A VNA will typically calculate these for you based on measurements/calibration and present them to you, therefore they can effectively be used to measure these values. Since Reflection coefficient is an S parameter and the others are normally calculated for you by a VNA, the best answer here is All these choices are correct.

Note that "network" in the name Vector Network Analyzer refers to electrical networks, not computer networks or communication networks. An electrical network is what you see on a schematic diagram.

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