**Attenuators**

Many times we are faced with the problem of needing a particular voltage for an application but the signal generator (or any other source) will not produce the desired voltage level. To solve this dilemma normally we could use a **voltage attenuator** using two resistors. The exact value of the resistors is not important because the level of the voltage can be adjusted using the signal generator amplitude control and the ratio of the two resistors.

__ __When using the signal generator to apply a voltage to an *energized* circuit, a capacitor *must* be placed between the signal generator and the circuit to block the circuit voltage from affecting the signal generator.

__ __

Figure No. 1.1 shows an attenuator. The voltage across *R*_{2} (*V*_{2}) could be applied to a circuit. This can be made to be of any value between the source voltage (*E*_{g}) and zero^{1}.

By applying the voltage divider rule to this circuit we obtain

(1.1)

Eq. 1.1 is the *attenuated *voltage of the source (*E*_{g} in this case). Notice that by choosing appropriate values for* R*_{1} and *R*_{2} the ratio (fraction)

(1.2)

can have a range between 0, when *R*_{2} = 0 or when *R*_{1} = ∞, and 1.0, when *R*_{1} = 0 or when *R*_{2} = ∞. Therefore, *V*_{2} can be made to
have a value between *E*_{g}and 0. If we keep the value of *R*_{1} constant, then *V*_{2} will depend only on *R*_{2} and *E*_{g}*.*

^{1} If, in theory, you replace *R*2 by a short circuit.

**Meter Loading**

When a measuring device is used to measure a value in a circuit (current or voltage) its impedance affects the measured value.

__ __

This is very similar to the *Uncertainty Principle *of Heisenberg in Quantum Physics. According to this principle^{2}, *“it is impossible to specify precisely and simultaneously the values of both members of particular pairs of physical variables that describe the behavior of an atomic system. In the Hamiltonian sense the members of these pairs of variables are canonically conjugate to each other”. *Or,

where ћ = *h/2π, *and *h* is Planck’s constant. (If you do not understand this statement, ask your lab instructor!)

__ __

This concept is called **meter loading**. The impedance of the measuring device changes the impedance of the circuit where the measurement is taking place. Thus, when applying the meter to the circuit to do the measurement, the circuit impedance (and thus the current and voltage) will change according to the value of the meter impedance. In order to diminish the meter effect when measuring a voltage in a circuit, the impedance of the meter should be very large^{3} with respect to the impedance across the measuring points^{4}.

In general, the oscilloscope has an impedance of the order of 10 *MΩ *when using the *X*10 probe, and an impedance around the 1 *MΩ* when using the *X*1 probe. Each oscilloscope, however, has different impedances. The reader should get this information about the level of these impedances by reading the manufacturer specifications of the oscilloscope and/or the probes available in the laboratory setting.

The VOMs, as well, have impedances that depend on the mode of operation. The level of impedance (or resistance) is different when measuring AC and DC voltages. When using a VOM in the laboratory, the reader should consult to the specifications of the instrument.

** How to measure voltages with an oscilloscope:**

To measure the voltage between two points in a circuit using the oscilloscope, the reader should follow one of the following two rules according to the measurement being made:

**One of the points is ***ground* – When measuring a voltage between point **a** and **ground,** just connect the connector cable from point **a** to channel 1 (or any other channel) of the oscilloscope. Because every channel of the oscilloscope is *grounded, *this procedure will give you the voltage between point **a** and **ground**.

**Neither point is ground **– If neither point **a** or point **b** is *ground*, then proceed as follows:

- Connect channel 1 of the oscilloscope to point
**a**^{5}**.** - Connect channel 2 of the oscilloscope to point
**b**. - Set the oscilloscope on the
**ADD **feature. - Set channel 2 to the
**invert** feature. - Make sure that the vertical sensitivity controls of both channels (volts/div) are in the same position
^{6}.

Following this procedure, we are actually measuring the voltage *V*_{ab} between points **a** and point **A** using the following known equation:

| *V*_{ab} = V_{a} – V_{b} | (1.3) |

where *V*_{a}and *V*_{b} are the voltages from **a** to ground and from **b** to ground respectively.

^{2} One of the most extraordinary and important achievements since the beginning of history.

^{3} Why? Answer this question in your lab report.

^{4} Normally we take the *rule of thumb* that the impedance of the meter should be at least ten times larger than the impedance in parallel with the measuring device.

^{5} Note that point **a** and point **b** can be any of the two points.

^{6} This should always be the case when using the **ADD** feature of the oscilloscope.

**Attenuators**

Many times we are faced with the problem of needing a particular voltage for an application but the signal generator (or any other source) will not produce the desired voltage level. To solve this dilemma normally we could use a **voltage attenuator** using two resistors. The exact value of the resistors is not important because the level of the voltage can be adjusted using the signal generator amplitude control and the ratio of the two resistors.

__ __When using the signal generator to apply a voltage to an *energized* circuit, a capacitor *must* be placed between the signal generator and the circuit to block the circuit voltage from affecting the signal generator.

__ __

Figure No. 1.1 shows an attenuator. The voltage across *R*_{2} (*V*_{2}) could be applied to a circuit. This can be made to be of any value between the source voltage (*E*_{g}) and zero^{1}.

By applying the voltage divider rule to this circuit we obtain

(1.1)

Eq. 1.1 is the *attenuated *voltage of the source (*E*_{g} in this case). Notice that by choosing appropriate values for* R*_{1} and...

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