THe original article was posted to TBL in the summer of 1996.
CABLE CAPACITANCE REVISITED: by Naoki Shibata
The result is interesting, I belive.
Before giving the results in detail, here's a brief table for gain per
cable cap. and freq:
---
100pF 300pF 600pF
40Hz -0.40dB -0.40dB -0.40dB
400Hz -0.40dB -0.39dB -0.37dB
1k -0.41dB -0.34dB -0.19dB
4kHz -0.91dB +0.27dB +2.1dB
10kHz -3.7dB -4.6dB -9.7dB
--
A cable with 50pF/meter cap is a fairly good instrument cable, and in
this case 100pF, 300pF and 600pF corresponds to cable of a length of
2m, 6m, 12m, respectively. For your information, 600pF at 1kHz and
10kHz has the impedance of 265k ohms and 26.5k ohms, respectively.
The comparison of the 10kHz gain tells us that 2m and 12m cable
varies significantly (6dB) between 100pF and 600pF. Even 300pF and
600pF comparison gives 5dB difference, which is too large to regard
"neglectable."
Small peaks are found at around 4kHz with 300pF and 600pF, these are
due to P.U. inductance and cable cap resonance. Guessing from the gain
at 6kHz, 4kHz-10kHz curve is rather decending, so you may hear the
difference... But these peaks are really new to me. Any opinion?
10kHz is surely too high for a bass' tone range, but what about the
spectrum at transient, especially playing in slapping style?
Here's a schematics of the approximated circuit I used.
----------------------------------------
+-+--+---+-+--+---+---+---+
| | | | | | | | |
R | | R | | | | |
| | Rv | | Rv Rt Cc |
L Rc | L Rc | | | Za
+-+ | +-+ | | | |
| | | | | | |
e | e | Ct | |
| | | | | | |
+----+---+----+---+---+---+
where
R = PU DC resistence, 7.3k ohms
L = 3.15H
e = ac voltage source
Rv = 250k ohms
Rt = 250k ohms
Rc = 1M ohms
Ct = 0.047 micro F(10^-6 F)
Cc = cable cap.
Za = 1Mohm (amp input impedance)
DC resistence and PU coil inductance are given by Bill Bolton.
Rc is a core loss resistence; the value can be examined in more
detail, but its main purpose is to introduce a limit of coil impedance
at very high frequencies.
-----------------------------------------
Here goes the simulation result (some stuffs deleted, though) from
SPICE.
******
* reading file: /.....
.option icsweep=1
.option parhier=global
.save type=nodeset level=all
v1 3 0 ac 1
r1 1 3 1meg
r2 2 3 7.3k
l1 1 2 3.15
v2 5 0 ac 1
r3 1 5 1meg
r4 4 5 7.3k
l2 1 4 3.15
r5 1 0 250k
r6 1 0 250k
r7 1 6 250k
c1 6 0 470n
r8 1 0 1meg
cc 1 0 ccc
.ac dec 5 1 1meg sweep data=aho
.plot ac vdb(1)
.data aho
ccc
100p
300p
600p
.enddata
.end
**warning** in element= 0:l1
inductance = 3.15 >= 0.1 henry, please verify it.
****** H S P I C E -- 95.2 (950213) 16:06:48 96/10/22 sun4
(DELETED)
******
shibata
****** ac analysis tnom= 25.000 temp= 25.000
******
Cable cap. = 100pF
freq vdb(1)
(a ) -60.0000 -40.0000 -20.0000 0. 20.0000
+ + + + +
1.0000 -321.689m-+------+------+------+------+------+------a------+------+-
1.5849 -348.877m + + + + + + a + +
2.5119 -372.507m + + + + + + a + +
3.9811 -387.033m + + + + + + a + +
6.3096 -394.151m + + + + + + a + +
10.0000 -397.255m + + + + + + a + +
15.8489 -398.542m + + + + + + a + +
25.1189 -399.074m + + + + + + a + +
39.8107 -399.315m + + + + + + a + +
63.0957 -399.483m + + + + + + a + +
100.0000 -399.732m-+------+------+------+------+------+------a------+------+-
158.4893 -400.287m + + + + + + a + +
251.1886 -401.652m + + + + + + a + +
398.1072 -405.071m + + + + + + a + +
630.9573 -413.654m + + + + + + a + +
1.0000k -435.206m + + + + + + a + +
1.5849k -489.303m + + + + + + a + +
2.5119k -624.903m + + + + + + a + +
3.9811k -963.139m + + + + + + a+ + +
6.3096k -1.791 + + + + + + a+ + +
10.0000k -3.681 -+------+------+------+------+------+---a--+------+------+-
15.8489k -7.291 + + + + + + a + + +
25.1189k -12.524 + + + + + a + + + +
39.8107k -18.411 + + + + +a + + + +
63.0957k -24.037 + + + + a + + + + +
100.0000k -29.050 + + + +a + + + + +
158.4893k -33.560 + + + a + + + + + +
251.1886k -37.785 + + + a + + + + + +
398.1072k -41.879 + + a+ + + + + + +
630.9573k -45.918 + + a + + + + + + +
1.0000x -49.933 -+------a------+------+------+------+------+------+------+-
+ + + + +
****** H S P I C E -- 95.2 (950213) 16:06:48 96/10/22 sun4
******
shibata
****** ac analysis tnom= 25.000 temp= 25.000
******
Cable cap. = 300pF
freq vdb(1)
(a ) -60.0000 -40.0000 -20.0000 0. 20.0000
+ + + + +
1.0000 -321.690m-+------+------+------+------+------+------a------+------+-
1.5849 -348.877m + + + + + + a + +
2.5119 -372.507m + + + + + + a + +
3.9811 -387.032m + + + + + + a + +
6.3096 -394.149m + + + + + + a + +
10.0000 -397.246m + + + + + + a + +
15.8489 -398.518m + + + + + + a + +
25.1189 -399.013m + + + + + + a + +
39.8107 -399.162m + + + + + + a + +
63.0957 -399.098m + + + + + + a + +
100.0000 -398.763m-+------+------+------+------+------+------a------+------+-
158.4893 -397.853m + + + + + + a + +
251.1886 -395.541m + + + + + + a + +
398.1072 -389.733m + + + + + + a + +
630.9573 -375.219m + + + + + + a + +
1.0000k -339.253m + + + + + + a + +
1.5849k -252.136m + + + + + + a + +
2.5119k -55.433m + + + + + + a + +
3.9811k 273.656m + + + + + + a + +
6.3096k -114.672m + + + + + + a + +
10.0000k -4.643 -+------+------+------+------+------+---a--+------+------+-
15.8489k -12.378 + + + + + a + + + +
25.1189k -20.130 + + + + a + + + +
39.8107k -27.163 + + + + a + + + + +
63.0957k -33.262 + + + a + + + + + +
100.0000k -38.466 + + +a + + + + + +
158.4893k -43.052 + + a + + + + + + +
251.1886k -47.308 + + a + + + + + + +
398.1072k -51.414 + a+ + + + + + + +
630.9573k -55.457 + a + + + + + + + +
1.0000x -59.474 -a------+------+------+------+------+------+------+------+-
+ + + + +
****** H S P I C E -- 95.2 (950213) 16:06:48 96/10/22 sun4
******
shibata
****** ac analysis tnom= 25.000 temp= 25.000
******
Cable cap. = 600pF
freq vdb(1)
(a ) -100.0000 -50.0000 0. 50.0000 100.0000
+ + + + +
1.0000 -321.690m-+------+------+------+------a------+------+------+------+-
1.5849 -348.877m + + + + a + + + +
2.5119 -372.507m + + + + a + + + +
3.9811 -387.031m + + + + a + + + +
6.3096 -394.144m + + + + a + + + +
10.0000 -397.232m + + + + a + + + +
15.8489 -398.483m + + + + a + + + +
25.1189 -398.922m + + + + a + + + +
39.8107 -398.933m + + + + a + + + +
63.0957 -398.522m + + + + a + + + +
100.0000 -397.314m-+------+------+------+------a------+------+------+------+-
158.4893 -394.210m + + + + a + + + +
251.1886 -386.386m + + + + a + + + +
398.1072 -366.732m + + + + a + + + +
630.9573 -317.412m + + + + a + + + +
1.0000k -193.922m + + + + a + + + +
1.5849k 112.860m + + + + a + + + +
2.5119k 845.115m + + + + a + + + +
3.9811k 2.084 + + + + +a + + + +
6.3096k -779.291m + + + + a + + + +
10.0000k -9.681 -+------+------+------+---a--+------+------+------+------+-
15.8489k -18.330 + + + + a + + + + +
25.1189k -26.168 + + + a + + + + +
39.8107k -33.196 + + + a + + + + + +
63.0957k -39.288 + + + a + + + + + +
100.0000k -44.489 + + + a + + + + + +
158.4893k -49.073 + + a + + + + + +
251.1886k -53.329 + + a+ + + + + + +
398.1072k -57.435 + + a + + + + + + +
630.9573k -61.477 + + a + + + + + + +
1.0000x -65.495 -+------+--a---+------+------+------+------+------+------+-
+ + + + +
---
The End.
Nicky
Kawasaki, Japan