#include <Filter6581.h>

Inheritance diagram for reSIDfp::Filter6581:

Collaboration diagram for reSIDfp::Filter6581:

Public Member Functions
void	setFilterCurve (double curvePosition)

Public Member Functions inherited from reSIDfp::Filter
	Filter (const FilterModelConfig &fmc, const Integrator &hpIntegrator, const Integrator &bpIntegrator)

uint16_t	clock (Voice &voice1, Voice &voice2, Voice &voice3)

void	enable (bool enable)

void	reset ()

void	writeFC_LO (uint8_t fc_lo)

void	writeFC_HI (uint8_t fc_hi)

void	writeRES_FILT (uint8_t res_filt)

void	writeMODE_VOL (uint8_t mode_vol)

void	input (int16_t input)

void	restart ()

Static Public Member Functions
static void	setFilterRange (double adjustment)

static void	enableOldCaps (bool enable)

Protected Member Functions
void	updateCenterFrequency () override

void	restartIntegrators () override

int32_t	getNormalizedMixerVoice (float v, uint8_t env) const override

Protected Member Functions inherited from reSIDfp::Filter
void	updateResonance (uint8_t res)

void	updateMixing ()

unsigned int	getFC () const

int32_t	getNormalizedVoice (float v, uint8_t env) const

Friends
class	State

Detailed Description

The SID filter is modeled with a two-integrator-loop biquadratic filter, which has been confirmed by Bob Yannes to be the actual circuit used in the SID chip.

Measurements show that excellent emulation of the SID filter is achieved, except when high resonance is combined with high sustain levels. In this case the SID op-amps are performing less than ideally and are causing some peculiar behavior of the SID filter. This however seems to have more effect on the overall amplitude than on the color of the sound.

The theory for the filter circuit can be found in "Microelectric Circuits" by Adel S. Sedra and Kenneth C. Smith. The circuit is modeled based on the explanation found there except that an additional inverter is used in the feedback from the bandpass output, allowing the summer op-amp to operate in single-ended mode. This yields filter outputs with levels independent of Q, which corresponds with the results obtained from a real SID.

We have been able to model the summer and the two integrators of the circuit to form components of an IIR filter. Vhp is the output of the summer, Vbp is the output of the first integrator, and Vlp is the output of the second integrator in the filter circuit.

According to Bob Yannes, the active stages of the SID filter are not really op-amps. Rather, simple NMOS inverters are used. By biasing an inverter into its region of quasi-linear operation using a feedback resistor from input to output, a MOS inverter can be made to act like an op-amp for small signals centered around the switching threshold.

In 2008, Michael Huth facilitated closer investigation of the SID 6581 filter circuit by publishing high quality microscope photographs of the die. Tommi Lempinen has done an impressive work on re-vectorizing and annotating the die photographs, substantially simplifying further analysis of the filter circuit.

The filter schematics below are reverse engineered from these re-vectorized and annotated die photographs. While the filter first depicted in reSID 0.9 is a correct model of the basic filter, the schematics are now completed with the audio mixer and output stage, including details on intended relative resistor values. Also included are schematics for the NMOS FET voltage controlled resistors (VCRs) used to control cutoff frequency, the DAC which controls the VCRs, the NMOS op-amps, and the output buffer.

SID filter / mixer / output

~~~ +------------------------------------------------—+ | | | +–1R1– --+ D7 | | +—R1–+ | | | | | | o–2R1– --o D6 | | +------—o–<A]–o–o | $17 | | | o–4R1– --o D5 1=open | (3.5R1) | | | | | | | +–8R1– --o D4 | (7.0R1) | | | | $17 | | (CAP2B) | (CAP1B) | 0=to mixer | +–R8–+ +—R8–+ +—C—o +—C—o 1=to filter | | | | | | | | +---—R8–o–o–[A>–o–Rw–o–[A>–o–Rw–o–[A>–o ve (EXT IN) | | | | D3 \ ------------—R8–o | | (CAP2A) | (CAP1A) | v3 | | vhp | vbp | vlp D2 | \ --------—R8–o +--—+ | | | | v2 | | | | D1 | | \ ----—R8–o | +-------------—+ | | | | v1 | | | | D0 | | | \ —R8–+ | | +------------------------—+ | | | | | | | R6 R6 R6 R6 R6* R6* R6* | | | | $18 | | | $18 | \ | | D7: 1=open \ \ \ D6 - D4: 0=open | | | | | | | +—o—o—o----------—o—o—+ 12V | | D3 +–/ –1R2–+ | | +—R8–+ | | +—R2–+ | | | | D2 o–/ –2R2–o | | ||–+ +—o–[A>–o---—o o–o–[A>–o–|| D1 o–/ –4R2–o (4.25R2) ||–+ $18 | | | 0=open D0 +–/ –8R2–+ (8.75R2) |
```
                                      vo (AUDIO
                                          OUT)
```
v1 - voice 1 v2 - voice 2 v3 - voice 3 ve - ext in vhp - highpass output vbp - bandpass output vlp - lowpass output vo - audio out [A> - single ended inverting op-amp (self-biased NMOS inverter) Rn - "resistors", implemented with custom NMOS FETs Rw - cutoff frequency resistor (VCR) C - capacitor
~~~ Notes:
```
R2  ~  2.0*R1
R6  ~  6.0*R1
R6* ~  1.07*R6
R8  ~  8.0*R1
R24 ~ 24.0*R1
```
The Rn "resistors" in the circuit are implemented with custom NMOS FETs, probably because of space constraints on the SID die. The silicon substrate is laid out in a narrow strip or "snake", with a strip length proportional to the intended resistance. The polysilicon gate electrode covers the entire silicon substrate and is fixed at 12V in order for the NMOS FET to operate in triode mode (a.k.a. linear mode or ohmic mode).

Even in "linear mode", an NMOS FET is only an approximation of a resistor, as the apparant resistance increases with increasing drain-to-source voltage. If the drain-to-source voltage should approach the gate voltage of 12V, the NMOS FET will enter saturation mode (a.k.a. active mode), and the NMOS FET will not operate anywhere like a resistor.

NMOS FET voltage controlled resistor (VCR)

~~~ Vw

| | R1 | +–R1–o | __|__ | --— | | | vi --—o-—+ +–o--— vo | | +-—R24-—+

vi - input vo - output Rn - "resistors", implemented with custom NMOS FETs Vw - voltage from 11-bit DAC (frequency cutoff control)
~~~ Notes:

An approximate value for R24 can be found by using the formula for the filter cutoff frequency:
```
FCmin = 1/(2*pi*Rmax*C)
```
Assuming that a the setting for minimum cutoff frequency in combination with a low level input signal ensures that only negligible current will flow through the transistor in the schematics above, values for FCmin and C can be substituted in this formula to find Rmax. Using C = 470pF and FCmin = 220Hz (measured value), we get:
```
FCmin = 1/(2*pi*Rmax*C)
Rmax = 1/(2*pi*FCmin*C) = 1/(2*pi*220*470e-12) ~ 1.5MOhm
```
From this it follows that: R24 = Rmax ~ 1.5MOhm R1 ~ R24/24 ~ 64kOhm R2 ~ 2.0*R1 ~ 128kOhm R6 ~ 6.0*R1 ~ 384kOhm R8 ~ 8.0*R1 ~ 512kOhm

Note that these are only approximate values for one particular SID chip, due to process variations the values can be substantially different in other chips.

Filter frequency cutoff DAC

~~~ 12V 10 9 8 7 6 5 4 3 2 1 0 VGND | | | | | | | | | | | | | Missing 2R 2R 2R 2R 2R 2R 2R 2R 2R 2R 2R 2R 2R termination | | | | | | | | | | | | | Vw –o-R-o-R-o-R-o-R-o-R-o-R-o-R-o-R-o-R-o-R-o-R-o- -+

Bit on: 12V Bit off: 5V (VGND)
~~~ As is the case with all MOS 6581 DACs, the termination to (virtual) ground at bit 0 is missing.

Furthermore, the control of the two VCRs imposes a load on the DAC output which varies with the input signals to the VCRs. This can be seen from the VCR figure above.

"Op-amp" (self-biased NMOS inverter)

~~~

                   12V

                    |
        +-----------o
        |           |
        |    +------o
        |    |      |
        |    |  ||--+
        |    +--||
        |       ||--+
    ||--+           |

vi --—|| o—o--— vo ||–+ | | | ||–+ | o----—|| | | ||–+ | ||–+ | | +–|| | | | ||–+ | | | | | | | +--------—o | | | | | | | GND | | | +-------------------—+

vi - input vo - output

~~~ Notes:

The schematics above are laid out to show that the "op-amp" logically consists of two building blocks; a saturated load NMOS inverter (on the right hand side of the schematics) with a buffer / bias input stage consisting of a variable saturated load NMOS inverter (on the left hand side of the schematics).

Provided a reasonably high input impedance and a reasonably low output impedance, the "op-amp" can be modeled as a voltage transfer function mapping input voltage to output voltage.

Output buffer (NMOS voltage follower)

~~~
```
       12V

        |
        |
    ||--+
```
vi --—|| ||–+ | o---— vo | (AUDIO Rext OUT) | |

GND

vi - input vo - output Rext - external resistor, 1kOhm
~~~ Notes:

The external resistor Rext is needed to complete the NMOS voltage follower, this resistor has a recommended value of 1kOhm.

Die photographs show that actually, two NMOS transistors are used in the voltage follower. However the two transistors are coupled in parallel (all terminals are pairwise common), which implies that we can model the two transistors as one.

Member Function Documentation

static void reSIDfp::Filter6581::enableOldCaps ( bool enable )

inlinestatic

Enable/disable old caps for 6581 model.

Parameters

enable true to enable old 2200pF caps, false to use new 470pF caps.

void reSIDfp::Filter6581::setFilterCurve ( double curvePosition )

Set filter curve type based on single parameter.

Parameters

curvePosition 0 .. 1, where 0 sets center frequency low ("dark") and 1 sets it high ("bright"). Default is 0.5

static void reSIDfp::Filter6581::setFilterRange ( double adjustment )

inlinestatic

Set filter offset and range based on single parameter.

Parameters

adjustment 0 .. 1, where 0 sets center frequency low ("dark"), 1 sets it high ("bright"). This also affects the range. Default is 0.5

void reSIDfp::Filter6581::updateCenterFrequency ( )

overrideprotectedvirtual

Set filter cutoff frequency.

Implements reSIDfp::Filter.

The documentation for this class was generated from the following files:

Filter6581.h
Filter6581.cpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Friends

Detailed Description

SID filter / mixer / output

NMOS FET voltage controlled resistor (VCR)

Filter frequency cutoff DAC

"Op-amp" (self-biased NMOS inverter)

Output buffer (NMOS voltage follower)

Member Function Documentation