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Resistive ladder divider.

Contents


Introduction.

Resistive ladder dividers are built from ( mostly ) same value resistors and have same output impedance from all taps if they are driven from a low impedance.
You can find a spread-sheet with the calculations here.


Resistive ladder divider.

Resistive ladder divider schematic.
Fig.1: Ladder divider.
(a): Basic circuit. If the output resistance is irrelevant, leave Rd out.
(b): Adding an "extra" Rb can in some cases reduce the tolerance requirement of Rc.
(c): If you are using arrays and have some resistors left over, adding them in the bottom of the ladder will further reduce the tolerance requirement of Rc.

This calculation assumes that Ra and k ( the gain factor ) are given:
Rb=k*Ra/(k^2-2*k+1).
Rc=k*Ra/(1-k).
Rd=k*Ra.
Re=1/(1/Rc-1/Rb).
Rin=Ra/(1-k).
Rout=Rd.

Rout and k given:
Ra=Rout/k.

Rin and k given:
Ra=Rin*(1-k).

Assuming Rc has the correct value::
k=(Ra+2*Rb-Ra*SQRT((Ra+4*Rb)/Ra))/(2*Rb).

To find standard values for Ra and Rb, use a voltage divider calculator like this one [1] and set:
Vin=1.
Vout=Rb/(Ra+Rb).

Table 1: Best Ra and Rb E24 values for different values of k.
kRaRbRcRdReRin
-0.5 dB160 Ω2.7 kΩ2.700 kΩ151.1 ΩN/A2.9 kΩ
-1 dB820 Ω62 kΩ6.720 kΩ730.8 Ω7.537 kΩ7.5 kΩ
-2 dB620 Ω2.4 kΩ2.395 kΩ492.5 Ω1 MΩ3.0 kΩ
-3 dB470 Ω3.9 kΩ1.139 kΩ332.7 Ω1.610 Ω1.6 kΩ
-4 dB1.1 kΩ5.1 kΩ1.881 kΩ694.1 Ω2.979 kΩ3.0 kΩ
-6 dB750 Ω1.5 kΩ753.6 Ω375.9 Ω1.514 kΩ1.5 kΩ
-8 dB910 Ω1.0 kΩ601.9 Ω362.3 Ω1.512 kΩ1.5 kΩ
-12 dB3.6 kΩ1.6 kΩ1.208 kΩ904.3 Ω4.924 kΩ4.8 kΩ
-16 dB1.2 kΩ270 Ω226.0 Ω190.2 Ω1.387 kΩ1.4 kΩ
-20 dB1.3 kΩ160 Ω144.4 Ω130.0 Ω1.486 kΩ1.4 kΩ
-32 dB6.8 kΩ180 Ω175.2 Ω170.8 Ω6.583 kΩ7.0 kΩ

References.

[1] Resistive voltage divider on mustcalculate.com.

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