Series Type Stepped Attenuators

bigpandahk · 2019-11-15 7:22 am

I want to build a 32 steps series attenuator but can't find a spreadsheet for calculating the resistor values. Goldpoint only have the values for 24 steps. Could anyone help please?

Please also recommend the brand / type resistor for the attenuator. Is SMD type resistor good?

Mark Tillotson · 2019-11-15 3:08 pm

How many dB per step? What impedance?

bigpandahk · 2019-11-15 3:10 pm

2dB, 50K or 100K

Thanks

Mark Tillotson · 2019-11-15 7:33 pm

I'll rattle out a Python program... Watch this space.

Mark Tillotson · 2019-11-15 8:02 pm

Code:

1:  10500.00 ohms   -2.05 dB
2:  8200.00 ohms   -4.07 dB
3:  6490.00 ohms   -6.09 dB
4:  5100.00 ohms   -8.09 dB
5:  4020.00 ohms   -10.07 dB
6:  3160.00 ohms   -12.02 dB
7:  2610.00 ohms   -14.05 dB
8:  2050.00 ohms   -16.06 dB
9:  1620.00 ohms   -18.06 dB
10:  1300.00 ohms   -20.09 dB
11:  1000.00 ohms   -22.05 dB
12:  820.00 ohms   -24.07 dB
13:  649.00 ohms   -26.09 dB
14:  510.00 ohms   -28.09 dB
15:  402.00 ohms   -30.07 dB
16:  316.00 ohms   -32.02 dB
17:  261.00 ohms   -34.05 dB
18:  205.00 ohms   -36.06 dB
19:  162.00 ohms   -38.06 dB
20:  130.00 ohms   -40.09 dB
21:  100.00 ohms   -42.05 dB
22:   82.00 ohms   -44.07 dB
23:   64.90 ohms   -46.09 dB
24:   51.00 ohms   -48.09 dB
25:   40.20 ohms   -50.07 dB
26:   31.60 ohms   -52.02 dB
27:   26.10 ohms   -54.05 dB
28:   20.50 ohms   -56.06 dB
29:   16.20 ohms   -58.06 dB
30:   13.00 ohms   -60.09 dB
31:   10.00 ohms   -62.05 dB
32:  39.00 ohms to ground
total 49960.5 ohms

Python code:

Code:

from math import log10

E48 = [
    1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40,
    1.47, 1.54, 1.62, 1.69, 1.78, 1.87, 1.96, 2.05,
    2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01,
    3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42,
    4.64, 4.87, 5.11, 5.36, 5.62, 5.90, 6.19, 6.49,
    6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53
]
E24 = [
    1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0,
    2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3,
    4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1
]
E12 = E24 [0:24:2]


def choose_best (value):
    best = None
    for p in range (6):
        for ent in E48:
            resistor = ent * pow(10, p)
            if best is None or abs(value-best) > abs(value-resistor):
                best = resistor
        for ent in E24:
            resistor = ent * pow(10, p)
            if best is None or abs(value-best) > abs(value-resistor):
                best = resistor
    return best

TOTAL_RESISTANCE = 50000
STEP = 2.0
STEP_COUNT = 32

def dB_2_ratio(dB):
    return pow(10.0, dB/20.0)


def calculate_steps(count, step, resistance):
    total = 0.0
    remaining_resistance = resistance
    target_resistance = resistance
    for i in range(1, count):
        target_resistance = remaining_resistance / dB_2_ratio (step)
        ideal_resistor = remaining_resistance - target_resistance
        actual_resistor = choose_best (ideal_resistor)
        total += actual_resistor
        remaining_resistance -= actual_resistor
        atten = 20.0 * log10 (remaining_resistance / resistance)
        print ("%s:  %6.2f ohms   %5.2f dB" % (i, actual_resistor, atten))

    print ("%s: %6.2f ohms to ground" % (count, choose_best (remaining_resistance)))
    print ("total %6.1f ohms" % total)

calculate_steps (STEP_COUNT, STEP, TOTAL_RESISTANCE)

Mark Tillotson · 2019-11-15 8:16 pm

BTW thin-film SMT are metal film, which are the most linear, but usually more expensive.
My code uses both E48 and E24 values, which might be an issue, can easily rework it.

PRR · 2019-11-15 8:34 pm

Loaded or unloaded?

A 100k pot is likely to be "loaded" in most systems unless a high-Z buffer is right after it.

For UN-loaded: re-write your dB as voltages. 0 -2 -4 -6 -8... becomes 0 0.794 0.631 0.501 0.398...

Say 100k. Then from -2dB tap to ground must be 100k*0.794 or 79.4k, and the 0 to -2 resistor must be 100k-79.4k or 20.6k. Go on from there.

Some cheats and checks. -6(.02)dB is half. So you know the sum of resistors above -6 must be 50k, and the sum below -6 must be 50k. Likewise -20 is 1/10 so top is 90k and bottom is 10k; -40dB is 1/100 so top must be 99k and bottom is 1k.

Mark Tillotson · 2019-11-15 10:50 pm

Unloaded, its just a discretized potentiometer. I'll add a load resistance option defaulting to 47k.

Mark Tillotson · 2019-11-15 11:46 pm

Code:

1:  5900.00 ohms    0.00 dB loaded by 47000,  0.00 dB unloaded
2:  6490.00 ohms   -2.00 dB loaded by 47000, -1.09 dB unloaded
3:  6490.00 ohms   -4.03 dB loaded by 47000, -2.46 dB unloaded
4:  6190.00 ohms   -6.04 dB loaded by 47000, -4.10 dB unloaded
5:  5360.00 ohms   -8.07 dB loaded by 47000, -6.01 dB unloaded
6:  4420.00 ohms   -10.07 dB loaded by 47000, -8.09 dB unloaded
7:  3480.00 ohms   -12.07 dB loaded by 47000, -10.29 dB unloaded
8:  2700.00 ohms   -14.06 dB loaded by 47000, -12.52 dB unloaded
9:  2050.00 ohms   -16.05 dB loaded by 47000, -14.76 dB unloaded
10:  1600.00 ohms   -18.02 dB loaded by 47000, -16.96 dB unloaded
11:  1210.00 ohms   -20.04 dB loaded by 47000, -19.17 dB unloaded
12:  953.00 ohms   -22.02 dB loaded by 47000, -21.32 dB unloaded
13:  715.00 ohms   -24.05 dB loaded by 47000, -23.49 dB unloaded
14:  562.00 ohms   -26.02 dB loaded by 47000, -25.57 dB unloaded
15:  442.00 ohms   -28.01 dB loaded by 47000, -27.64 dB unloaded
16:  348.00 ohms   -30.00 dB loaded by 47000, -29.72 dB unloaded
17:  270.00 ohms   -32.02 dB loaded by 47000, -31.79 dB unloaded
18:  215.00 ohms   -34.01 dB loaded by 47000, -33.82 dB unloaded
19:  169.00 ohms   -36.02 dB loaded by 47000, -35.87 dB unloaded
20:  133.00 ohms   -38.03 dB loaded by 47000, -37.92 dB unloaded
21:  105.00 ohms   -40.04 dB loaded by 47000, -39.95 dB unloaded
22:   82.50 ohms   -42.04 dB loaded by 47000, -41.97 dB unloaded
23:   64.90 ohms   -44.03 dB loaded by 47000, -43.97 dB unloaded
24:   51.10 ohms   -46.01 dB loaded by 47000, -45.96 dB unloaded
25:   42.20 ohms   -47.96 dB loaded by 47000, -47.92 dB unloaded
26:   33.00 ohms   -49.99 dB loaded by 47000, -49.96 dB unloaded
27:   26.10 ohms   -52.00 dB loaded by 47000, -51.97 dB unloaded
28:   20.50 ohms   -54.00 dB loaded by 47000, -53.98 dB unloaded
29:   16.20 ohms   -55.98 dB loaded by 47000, -55.96 dB unloaded
30:   13.00 ohms   -57.94 dB loaded by 47000, -57.93 dB unloaded
31:   10.50 ohms   -59.92 dB loaded by 47000, -59.91 dB unloaded
32:   40.20 ohms   -61.94 dB loaded by 47000, -61.93 dB unloaded
total 50202.2 ohms

With reworked code using a load resistance:

Code:

from math import log10, sqrt

E48 = [
    1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40,
    1.47, 1.54, 1.62, 1.69, 1.78, 1.87, 1.96, 2.05,
    2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01,
    3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42,
    4.64, 4.87, 5.11, 5.36, 5.62, 5.90, 6.19, 6.49,
    6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53
]
E24 = [
    1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0,
    2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3,
    4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1
]
E12 = E24 [0:24:2]


def choose_best (value, res_values):
    best = None
    for p in range (6):
        for ent in res_values:
            resistor = ent * pow(10, p)
            if best is None or abs(value-best) > abs(value-resistor):
                best = resistor
    return best


def dB_2_ratio(dB):
    return pow(10.0, dB/20.0)

def ratio_2_dB(num, denom):
    return 20.0 * log10 (num / denom)


def calc_loaded_resistances (total, load, ratio):
    # Split a total resistance for a given voltage ratio when loaded by load - quadratic solving
    a = -ratio
    b = ratio * total - load
    c = ratio * total * load
    temp = b*b - 4*a*c
    lower = (-b - sqrt(temp)) / (2*a)
    upper = total - lower
    return upper, lower


def parallel (r1, r2):
    # utility fn for combining impedances
    return r1 * r2 / (r1 + r2)


def calculate_steps(count, step, resistance, res_values, load = 47000.0):
    # first calculate ideal resistances in chain
    target_ratio = 1.0
    ideal_resistors = []
    last_upper = 0.0
    for i in range(1, count):
        target_ratio /= dB_2_ratio (step)
        upper, lower = calc_loaded_resistances (resistance, load, target_ratio)
        ideal_resistors.append (upper - last_upper)
        last_upper = upper

    # fit closest available values
    actual_resistors = []
    for i in range (1, count):
        actual_resistors.append (choose_best (ideal_resistors[i-1], res_values))
    actual_resistors.append (choose_best (lower, res_values))

    # calculate actual attenuation factors, loaded or unloaded
    total = 0.0
    remaining_resistance = sum (actual_resistors)
    i = 1
    for act in actual_resistors:
        atten = ratio_2_dB (parallel (remaining_resistance, load), total + parallel (remaining_resistance, load))
        unload_atten = ratio_2_dB (remaining_resistance, remaining_resistance + total)
        print ("%s:  %6.2f ohms   %5.2f dB loaded by %i, %5.2f dB unloaded" % (i, act, atten, load, unload_atten))
        total += act
        remaining_resistance -= act
        i += 1

    print ("total %6.1f ohms" % total)

calculate_steps (32, 2, 50000, E48+E24)
# calculate_steps (32, 2, 50000, E24)

bigpandahk · 2019-11-16 12:11 am

thanks Mark for the great code.

also thanks PRR's advice.

bigpandahk · 2019-11-16 12:46 am

My friend gave me a pair of this excellent switches.

merlin el mago · 2019-11-16 1:55 pm

Wow I use the same Shallco but mine is motorized with only 32 steps. I believe is the best switch money can buy.

bigpandahk · 2019-11-16 2:28 pm

Motorised!! Can mine be modified?

bigpandahk · 2019-11-16 2:29 pm

@Mark Tillotson

Mark, your code is excellent and very easy to change the parameters. Thanks a lot.

Bigman80 · 2019-11-16 2:56 pm

merlin el mago said:
Wow I use the same Shallco but mine is motorized with only 32 steps. I believe is the best switch money can buy.

Why? What makes it so good?

Genuinely interested

PRR · 2019-11-16 5:54 pm

> What makes it so good?

The Shallcross/Shallco (and another brand, Daven, also IRC) were PROFESSIONAL attenuators invented in the 1930s for talking-movie and broadcast applications, where reliability was more important than the cost. Find pictures online. Solid contacts with selected metal plating, real springs, solid wafers.
http://www.technicalaudio.com/pdf/Daven/Daven_attenuator_switch_lab_Catalog.pdf

Mark Tillotson · 2019-11-16 6:56 pm

bigpandahk said:
@Mark Tillotson

Mark, your code is excellent and very easy to change the parameters. Thanks a lot.

I found the loaded case is a little trickier as a quadratic has to be solved, but you should do your mental pressups regularly, algebra, coding, whatever.

merlin el mago · 2019-11-16 8:33 pm

bigpandahk said:
Motorised!! Can mine be modified?

I don't know, it's 23 steps (I'm sorry my mistake), I bought mine here: BentAudio.com :: TAP

bigpandahk · 2019-11-29 7:04 am

Finished the first one

Series Type Stepped Attenuators

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