Humbuckers and Multiple Pickups with LTSpice Delay

[aquin43]

The inter-pole spacing of a humbucker or the spacing of two or more pickups can be modelled in LTSpice by treating the string as a delay line. The delay per unit length of the string is 1/(2*f0*scale) where f0 is the open string frequency and scale is the scale length. The inter-pole delay is the pole or pickup spacing times this. The delay line device in LTspice is called "tline".

Here is a schematic that represents the source driving the delay and being summed with the delayed signal. The parameters are for the bottom E string on a Gibson scale length with a standard Humbucker. Parameter (.param) statements are used to set the variables. I used millimetres, but inches would work just as well. The output is scaled to give zero dB at low frequencies.





This is a listing of the source file for the schematic, delay.asc

Version 4
SHEET 1 920 680
WIRE 704 -80 656 -80
WIRE 656 -64 656 -80
WIRE 608 -48 -48 -48
WIRE 608 0 560 0
WIRE 560 32 560 0
WIRE -48 48 -48 -48
WIRE 0 48 -48 48
WIRE 144 48 80 48
WIRE 400 48 240 48
WIRE 512 48 400 48
WIRE 144 80 96 80
WIRE 320 80 240 80
WIRE -48 96 -48 48
WIRE 400 96 400 48
WIRE 512 96 480 96
WIRE -48 224 -48 176
WIRE 96 224 96 80
WIRE 96 224 -48 224
WIRE 320 224 320 80
WIRE 320 224 96 224
WIRE 400 224 400 176
WIRE 400 224 320 224
WIRE 480 224 480 96
WIRE 480 224 400 224
WIRE 560 224 560 112
WIRE 560 224 480 224
WIRE 608 224 560 224
WIRE 656 224 656 16
WIRE 656 224 608 224
WIRE 608 256 608 224
FLAG 608 256 0
FLAG 704 -80 out
SYMBOL tline 192 64 R0
WINDOW 3 15 17 Top 2
SYMATTR InstName T1
SYMATTR Value Td={dely} Z0=50
SYMBOL voltage -48 80 R0
WINDOW 3 8 160 Left 2
WINDOW 123 12 101 Left 2
WINDOW 39 0 0 Left 0
SYMATTR Value ""
SYMATTR Value2 AC 1
SYMATTR InstName V1
SYMBOL res 96 32 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R1
SYMATTR Value 50
SYMBOL res 384 80 R0
SYMATTR InstName R2
SYMATTR Value 50
SYMBOL e 560 16 R0
WINDOW 0 -40 5 Left 2
SYMATTR InstName E1
SYMATTR Value -2
SYMBOL e 656 -80 R0
WINDOW 0 -41 8 Left 2
SYMATTR InstName E2
SYMATTR Value 0.5
TEXT -56 296 Left 2 !.ac dec 100 80 10k
TEXT 192 256 Left 2 !.param f0 = 82.4
TEXT 192 280 Left 2 !.param scale = 628.6
TEXT 192 304 Left 2 !.param psep = 17
TEXT 192 328 Left 2 !.param dely = psep/(2*f0*scale)


The transient response could also be plotted.

Arthur

[antigua]

Wow, it's nice to see comb filtering considered in LTSpice in addition to the usual RLC plots. This seems to be similar in effect to this tool www.till.com/articles/PickupResponseDemo/ , but in your demo I don't see how the pickup's offset distance from the bridge is accounted for. According to the Tillman demo, the frequency of the first dip will be higher just by shifting the pickups closer to the bridge. 

[aquin43]

This is just the intrinsic response of the pickup to a string with a given delay per unit length. The overall response to a string pluck will be this multiplied by the waveform spectrum presented to the pickup, which depends on its position along the string.

The magneto electric response that we usually measure is similarly intrinsic to the pickup and would have to be multiplied in as well for the full response.

Arthur

[pablogilberto]

Apr 10, 2020 12:43:40 GMT -5 antigua said:

Wow, it's nice to see comb filtering considered in LTSpice in addition to the usual RLC plots. This seems to be similar in effect to this tool www.till.com/articles/PickupResponseDemo/ , but in your demo I don't see how the pickup's offset distance from the bridge is accounted for. According to the Tillman demo, the frequency of the first dip will be higher just by shifting the pickups closer to the bridge. 

Hi antigua

Can you help me understand this comb filtering thing?

I also don't know how to use the tool? www.till.com/articles/PickupResponseDemo/

Right now, I understand the RLC, resonant freq of pickups.

I want to know how can I use this comb filtering to deepen my understanding.

Thank you

[aquin43]

A string and pickup modelled as forward and backward delays with reflections at the nut and bridge.

The forward path is T1, T2 and T3 and the reverse path is T4, T5 and T6. The fundamental frequency is set to 1Hz for convenience.

The idea is that the string behaves as a delay line. The pluck signal travels in both directions until it meets either the bridge or the nut (or a fret). Because the nut and bridge are stiff compared with the string, the major part of the signal is reflected in inverted form. The reflection coefficient is set to 0.995 (refc). In the model, each path is split and controlled E sources are used to make the delay lines unidirectional. In addition, matching resistors are used, each of which causes a loss of a half. These losses are made up by the 2X gain multipliers in the E sources.

The feedback round the loop makes the string very sensitive at certain frequencies, determined by the delays which, in turn, are determined by the pluck and pickup positions. The pickup response is the sum of the forward and backward waves at its position. In the model, here scaled down by 2 to make the peaks 0db.

The diagram below shows both the resonant frequencies of the delay line system and the pickup response divided by the string excitation for a pluck in the centre of the string with the pickup at 0.3 of the string length from the bridge. Note the absence of even harmonics. The peaks are very narrow so their heights will depend on how well the sampling frequencies  coincide with them.

This model is based on the discussion in

www.researchgate.net/profile/Vesa_Vaelimaeki/publication/234034228_Acoustics_and_Modeling_of_Pickups/links/00463528773062047c000000/Acoustics-and-Modeling-of-Pickups.pdf

Arthur