Attenuator (electronics)

Not to be confused with Squelch.
A 30 dB 5W RF-attenuator, DC-18GHz, with N-type coaxial connectors
Coaxial Dynamics 100 Watt power attenuator

An attenuator is an electronic device that reduces the power of a signal without appreciably distorting its waveform.

An attenuator is effectively the opposite of an amplifier, though the two work by different methods. While an amplifier provides gain, an attenuator provides loss, or gain less than 1.

Construction and usage

Attenuators are usually passive devices made from simple voltage divider networks. Switching between different resistances forms adjustable stepped attenuators and continuously adjustable ones using potentiometers. For higher frequencies precisely matched low VSWR resistance networks are used.

Fixed attenuators in circuits are used to lower voltage, dissipate power, and to improve impedance matching. In measuring signals, attenuator pads or adapters are used to lower the amplitude of the signal a known amount to enable measurements, or to protect the measuring device from signal levels that might damage it. Attenuators are also used to 'match' impedance by lowering apparent SWR.

Attenuator circuits

π-type unbalanced attenuator circuit
π-type balanced attenuator circuit
T-type unbalanced attenuator circuit
T-type balanced attenuator circuit

Basic circuits used in attenuators are pi pads (π-type) and T pads. These may be required to be balanced or unbalanced networks depending on whether the line geometry with which they are to be used is balanced or unbalanced. For instance, attenuators used with coaxial lines would be the unbalanced form while attenuators for use with twisted pair are required to be the balanced form.

Four fundamental attenuator circuit diagrams are given in the figures on the left. Since an attenuator circuit consists solely of passive resistor elements, it is linear and reciprocal. If the circuit is also made symmetrical (this is usually the case since it is usually required that the input and output impedance Z1 and Z2 are equal) then the input and output ports are not distinguished, but by convention the left and right sides of the circuits are referred to as input and output, respectively.

Attenuator characteristics

A RF Microwave Attenuator. Picture courtesy of Herley

Key specifications for attenuators are:[1]

RF attenuators

Radio frequency attenuators are typically coaxial in structure with precision connectors as ports and coaxial, micro strip or thin-film internal structure. Above SHF special waveguide structure is required.

Important characteristics are:

The size and shape of the attenuator depends on its ability to dissipate power. RF attenuators are used as loads for and as known attenuation and protective dissipation of power in measuring RF signals.[2]

Audio attenuators

A line-level attenuator in the preamp or a power attenuator after the power amplifier uses electrical resistance to reduce the amplitude of the signal that reaches the speaker, reducing the volume of the output. A line-level attenuator has lower power handling, such as a 1/2-watt potentiometer or voltage divider and controls preamp level signals, whereas a power attenuator has higher power handling capability, such as 10 watts or more, and is used between the power amplifier and the speaker.

Component values for resistive pads and attenuators

This section concerns pi-pads, T-pads and L-pads made entirely from resistors and terminated on each port with a purely real resistance.

Reference figures for attenuator component calculation

This circuit is used for the general case, all T-pads, all pi-pads and L-pads when the source impedance is greater than or equal to the load impedance.
The L-pad computation assumes that port 1 has the highest impedance. If the highest impedance happens to be the output port, then use this figure.
Unique resistor designations for Tee, Pi and L pads.

The attenuator two-port is generally bidirectional. However in this section it will be treated as though it were one way. In general, either of the two figures above applies, but the figure on the left (which depicts the source on the left) will be tacitly assumed most of the time. In the case of the L-pad, the right figure will be used if the load impedance is greater than the source impedance.

Each resistor in each type of pad discussed is given a unique designation to decrease confusion.

The L-pad component value calculation assumes that the design impedance for port 1 (on the left) is equal or higher than the design impedance for port 2.

Terms used

Symbols used

Passive, resistive pads and attenuators are bidirectional two-ports, but in this section they will be treated as unidirectional.

Symmetric T pad resistor calculation

A = 10^{-Loss/20} \qquad R_a = R_b = Z_S \frac {1 - A} {1 + A} \qquad R_c = \frac {Z_s^2 - R_b^2 } {2 R_b } \qquad \, see Valkenburg p 11-3[3]

Symmetric pi pad resistor calculation

A = 10^{-Loss/20} \qquad R_x = R_y = Z_S \frac {1 + A} {1 - A} \qquad R_z = \frac {2R_x}{\left ( \frac {R_x}{Z_S} \right ) ^2 -1} ]\qquad \, see Valkenburg p 11-3[3]

L-Pad for impedance matching resistor calculation

If a source and load are both resistive (i.e. Z1 and Z2 have zero or very small imaginary part) then a resistive L-pad can be used to match them to each other. As shown, either side of the L-pad can be the source or load, but the Z1 side must be the side with the higher impedance.

R_q = \frac {Z_m} {\sqrt{\rho - 1}} \qquad R_p = Z_m \sqrt {\rho - 1}
\text{Loss} = 20 \log_{10} \left(\sqrt{\rho - 1} + \sqrt{\rho }\right) \quad \text{where} \quad \rho = \frac {Z_1}{Z_2} \quad Z_m = \sqrt{ Z_1 Z_2} \text{ } \, see Valkenburg p 11-3[4]

Large positive numbers means loss is large. The loss is a monotonic function of the impedance ratio. Higher ratios require higher loss.

Converting T-pad to pi-pad

This is the Y-Δ transform

R_z = \frac {R_a R_b + R_a R_c + R_b R_c} {R_c} \qquad R_x = \frac {R_a R_b + R_a R_c + R_b R_c} {R_b} \qquad R_y = \frac {R_a R_b + R_a R_c + R_b R_c} {R_a}. \qquad \, [5]

Converting pi-pad to T-pad

This is the Δ-Y transform

R_c = \frac {R_x R_y} {R_x + R_y + R_z} \qquad R_a = \frac {R_z R_x} {R_x + R_y + R_z} \qquad R_b = \frac {R_z R_y} {R_x + R_y + R_z} \qquad \, [5]

Conversion between two-ports and pads

T-pad to impedance parameters

The impedance parameters for a passive two-port are
V_1 = Z_{11} I_1 + Z_{12} I_2 \qquad V_2 = Z_{21} I_1 + Z_{22} I_2 \qquad \text{with} \qquad Z_{12} = Z_{21} \,
It is always possible to represent a resistive t-pad as a two-port. The representation is particularly simple using impedance parameters as follows:
Z_{21} = R_c \qquad Z_{11} = R_c + R_a \qquad Z_{22} = R_c + R_b \,

Impedance parameters to T-pad

The preceding equations are trivially invertible, but if the loss is not enough, some of the t-pad components will have negative resistances.
R_c = Z_{21} \qquad R_a = Z_{11} - Z_{21} \qquad R_b = Z_{22} - Z_{21} \,

Impedance parameters to pi-pad

These preceding T-pad parameters can be algebraically converted to pi-pad parameters.
R_z = \frac { Z_{11}Z_{22} - Z_{21}^2 } {Z_{21} } \qquad R_x = \frac { Z_{11}Z_{22} - Z_{21}^2 } {Z_{22} - Z_{21} } \qquad R_y = \frac { Z_{11}Z_{22} - Z_{21}^2 } {Z_{11} - Z_{21} } \qquad

Pi-pad to admittance parameters

The admittance parameters for a passive two port are
I_1 = Y_{11} V_1 + Y_{12} V_2 \qquad I_2 = Y_{21} V_1 + Y_{22} V_2 \qquad \text{with} \qquad Y_{12} = Y_{21} \,
It is always possible to represent a resistive pi pad as a two-port. The representation is particularly simple using admittance parameters as follows:
Y_{21} = \frac {1} { R_z } \qquad Y_{11} = \frac {1} {R_x} + \frac {1} { R_z } \qquad Y_{22} = \frac {1} {R_y} + \frac {1} { R_z } \,

Admittance parameters to pi-pad

The preceding equations are trivially invertible, but if the loss is not enough, some of the pi-pad components will have negative resistances.
R_z = \frac {1} {Y_{21}} \qquad R_x = \frac {1} {Y_{11} - Y_{21} } \qquad R_y = \frac {1} {Y_{22} - Y_{21} } \,


General case, determining impedance parameters from requirements

Because the pad is entirely made from resistors, it must have a certain minimum loss to match source and load if they are not equal.

The minimum loss is given by

Loss_{min} = 20 \ log_{10} \left ( \sqrt{ \rho - 1 } + \sqrt{\rho } \quad \right ) \, \quad \text{where} \quad \rho = \frac {\max [ Z_S, Z_{Load} ]}{\min [ Z_S, Z_{Load} ] } \, [3]

Although a passive matching two-port can have less loss, if it does it will not be convertible to a resistive attenuator pad.

A = 10^{-Loss/20} \qquad Z_{11} = Z_S \frac {1+A^2} {1-A^2} \qquad Z_{22} = Z_{Load} \frac {1+A^2} {1-A^2} \qquad Z_{21} = 2 \frac { A \sqrt { Z_S Z_{Load}}} {1-A^2} \,

Once these parameters have been determined, they can be implemented as a T or pi pad as discussed above.

See also

Notes

References

External links

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