Passive L-pad Attenuator
In its most basic form, the L-pad Attenuator
is nothing more than a very simple voltage divider
circuit used in many electrical and electronic circuits to generate a
lower voltage. The difference this time is that this type of
attenuator is used in frequency dependant circuits to create loss
(attenuation) in a transmission line or to match the impedances
of unbalanced source and load networks. The L-pad attenuator
consists of two purely resistive elements in series with each
other connected across a voltage source with the ratio between these two
resistances forming a voltage divider network as shown below.
Basic L-pad Attenuator Circuit
We can see that the L-pad attenuator design is identical to the voltage divider circuit used to reduce its
input voltage by some amount. The two resistors are connected in series across the whole of the input voltage, while the output
signal or voltage is taken across just one resistance, with the two resistive elements forming the shape of an inverted letter
"L" and hence their name, "L-pad Attenuators". For this types of circuit, attenuation is given as Vout/Vin.
Input resistor R1 is in series with the output, while resistor R2
is in parallel with the output and therefore the load. Then the output
voltage provided by this "L" shaped arrangement is divided by a
factor equal to the ratio of these two resistor values as shown.
As the L-pad attenuator is made of purely resistive
components, there is no phase shift in the attenuator.
The insertion of the attenuator between the source and the load must not
alter the source voltage and therefore the resistance
seen by the source must remain the same at all times. As the two
resistive elements have constant values, if the impedance of the
load is not infinite, the attenuation is altered and so to is its
impedance. As a result the L-pad attenuator can only supply an
impedance match in one direction only.
L-pad attenuators are commonly used in audio applications to reduce a larger or more
powerful signal while matching the impedance between the source and load in provide maximum power transfer. However, if the
impedance of the source is different to the impedance of the load, the L-pad attenuator can be made to match either impedance
but not both. This is because the arrangement of the resistive elements does not produce the same impedance looking into the
network from both directions. In other words, the L-pad attenuator is an asymmetrical attenuator and therefore, if an
attenuation network is required to match two unequal impedances in both directions, other types of attenuator such as the
symmetrical "T-pad" or the "Pi-pad" attenuator should be used.
L-pad Attenuator with Equal Impedances
As mention previously, a passive attenuator is a
resistive network designed to reduce the power or signal level
of an audio or radio frequency signal without introducing any distortion
to the signal. Sometimes the output from an audio amplifier
maybe too high and attenuation is required to feed this signal into a
loudspeaker. For example lets assume we want to reduce the
power being delivered from an amplifier which has an output source
impedance, ( ZS )
of 8Ω feeding a loudspeaker load, ( ZL ) of 8Ω by 6dB. The values of resistors
R1 and R2 are as follows.
L-pad Attenuator Circuit
The equation for the L-pad attenuator circuit connected between two equal impedances,
( ZS = ZL ) looking in the direction of the source impedance,
ZS will be.
To simplify the design of the attenuator, a "K" value can be
used in the attenuator equation above to simplify the maths a little. This "K" value is
the ratio of the voltage, current or power corresponding to a given value of attenuation. The general equation for
"K" is given as:
Then in our example the "K" value for a voltage attenuation of 6dB
will be 10(6/20) = 1.9953. Substituting this value for attenuation into the two equations gives.
Then between two equal impedances looking in the direction of the source impedance ZS,
the value of the series resistor, R1 is 4Ω and the value of the parallel resistor,
R2 is 8Ω.
The problem with this type of L-pad attenuator configuration is that the impedance match is in the
direction of the series resistor R1, while the impedance "mismatch" is towards the parallel
resistor R2. The problem with this is that as the level of attenuation is increased this mismatch
becomes increasingly larger and at high values of attenuation the value of the parallel resistor will become fractions of an
Ohm. For example, the values of R1 and R2 at an attenuation of -32dB would
be 7.8Ω and 0.2Ω, that's 200mΩ effectively shorting out the loudspeaker which could have a serious effect on
the amplifiers output circuitry.
One way to increase attenuation without overloading the source is to impedance match the circuit in the direction
of the load impedance, ZL. However,
as we are now looking into the L-pad attenuator circuit
from the parallel resistor side, the equations are slightly different.
Then between equal impedances and with the impedance match
looking from the load, the values or resistors R1 and R2 are calculated as follows.
"Looking" from the Load
If we know increase attenuation to -32dB, the value of the resistors will become, R1 = 310Ω and R2 = 8.2Ω
respectively, and these values are safe enough for the source circuit to which it is connected.
L-pad Attenuator with Unequal Impedances
Thus far we have looked at connecting the L-pad Attenuator between to equal impedances in
order to provide attenuation of a signal. But we can also use the "L-pad attenuator" to match the impedances of two unequal
circuits. This impedance match may be in the direction of the larger or the smaller impedance but not both. The configuration
of the attenuator will be the same as before, but the equations used in matching the two unequal impedances are different as
shown.
Between two unequal impedances, the impedance matching is towards the smaller of the two impedances from the source.
Impedance Match towards the small Impedance
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Between two unequal impedances, the impedance matching is towards the larger of the two impedances from the load.
Impedance Match towards the larger Impedance
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Example No2
A signal transmission line which has a source impedance of 75Ω is to be connected
to a signal strength meter of impedance 50Ω which has a maximum display of -12dB. Calculate the values
of resistors required in an L-pad attenuator circuit to operate the meter at maximum power.
With the impedance match towards the smaller 50Ω value, resistors R1 and
R2 are calculated as follows.
Then resistor R1 is equal to 59.6Ω and R2 is equal to
22.2Ω, or the nearest preferred values.
The L-pad attenuator can be used to
perfectly match one impedance to another providing a fixed
amount of attenuation, but the resulting circuit is "lossy". However, if
a fixed amount of attenuation is of no importance and only
the minimum insertion loss is required between the source and the load,
the L-pad attenuator can be used to match
two impedances of unequal values using the following equations to calculate resistors, R1 and
R2.
Minimum Insertion Loss
Where: resistor R1 is on the side of the larger impedance and resistor R2
is on the side of the smaller impedance and in our example above that would be 75Ω and 50Ω respectively. The minimum insertion
loss in decibels of an L-pad attenuator connected between a source and a load is therefore given as:
Minimum Attenuation in dB
L-pad Attenuator Summary
In this tutorial we have seen that a L-pad attenuator
circuit is a passive and purely resistive
network which can be used to reduce the strength of a signal while
matching the impedances of the source and load. L-pad attenuators
are commonly used in audio electronics to reduce the audio signal
produced by an amplifier delivered to a speaker or headphones.
However, one of the main disadvantages of the "L-pad attenuator" is that
because the L-pad attenuator is a constant impedance device,
at low power settings the attenuator converts all of the energy not sent
to the load into heat which can be considerable. Also, at
much higher frequencies or where an attenuator circuit is required
perfectly match the input and output, other improved
attenuator designs are used.
In the next tutorial about Attenuators, we will look at another type of attenuator design
called the T-pad Attenuator that uses three resistive components to produced a balanced attenuator.
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