Analog Computer: Math Extension Module

This repository provides a math extension module for analog computing applications. The module provides two absolute value functions, two square-root functions, and one logarithmic value function (base $10$ and $e$) of the input. Each output features an indicator LED that provides visual feedback proportional to the output value.

Module Schematic

Absolute function(x): $x \rightarrow |x|$

The circuit for the absolute value function incorporates two different designs.

The left circuit is based on individual diodes and represents the classical implementation of an absolute value circuit. This circuit follows the design outlined in the document PRECISION ABSOLUTE VALUE CIRCUITS from BURR-BROWN/TI.

The right circuit is similar but with one important difference: the diodes are replaced with P-channel MOSFETs on a single substrate. This should ensure thermal coupling and closely specifications of the two MOSFETs.

Square-Root function(x): $x \rightarrow \sqrt{x}$

The circuit implementation of the square-root function is based on the feedback principle. A multiplier squares the output signal and feeds it back into an open-loop amplifier to yield the inverse function. The diode in the feedback path ensures that only negative values are allowed at the input; otherwise, the output remains close to zero, preventing overload. For ease of use, an inverter is placed before the input, resulting in the overall transfer function of the module:

$$ \begin{align} f(x) = \begin{cases} \sqrt{x} & \text{if } x > 0 \\ 0 & \text{if } x \le 0 \end{cases} \end{align} $$

This circuit design is based on the schematic and principals presented in the book Analog and Hybrid Computer Programming by Prof. Dr. Bernd Ulmann and the book on the THAT Analog Computer by Michael Koch.

Logarithmic function(x): $x \rightarrow \mathrm{log}{10}(x)$ and $x \rightarrow \mathrm{log}{e}(x)$

The logarithm function circuit is based on the LOG200 chip from Texas Instruments. The input voltage must be scaled down from $\pm 10 , V$ to the chip's maximum accepted range of $\pm 5 , V$. According to the datasheet, $-5V$ falls within the absolute maximum ratings and will not damage the chip.

The transfer function of the LOG200 chip is

$$ V_\mathrm{LOG} = 250 , mV \cdot \mathrm{log}_{10} \left( \frac{I_1}{I_2} \right) $$

which depends on the ratio of the input currents $I_1$ and $I_2$. The input current $I_2$ is wired to the internal $1 , \mu A$ precision current source. Accordingly, the input voltage has to be scaled using a precision (0.05%) $50k\Omega$ resistor to give the appropriate current $I_1$. Since we want to map the output to the full range of our machine unit, $\pm1$ or $\pm 10 ,V$, a "20x" amplifier is placed after the output of the Voltage $V_\mathrm{LOG}$.

With this scaling, the following input-output relationship is achieved:

Input	Current $I_1$	Output of LOG200	Circuit Output
$0.001 , V$	$0.01 , \mu A$	$-0.5,V$	$-10 , V$
$0.01 , V$	$0.1 , \mu A$	$-0.25,V$	$-5 , V$
$0.1 , V$	$1 , \mu A$	$0,V$	$0 , V$
$1 , V$	$10 , \mu A$	$0.25,V$	$5 , V$
$10 , V$	$100 , \mu A$	$0.5,V$	$10 , V$

To additionally compute the natural logarithm $\mathrm{log}_e$, we use the relation:

$$ \mathrm{log}{e}(x) = \frac{\mathrm{log}{10}(x)}{\mathrm{log}{10}(e)} = 2.303 \cdot \mathrm{log}{10}(x) $$

A simple scaling amplifier with a gain of $0.2303x$ is used to provide the output of $\mathrm{log}_e(x) / 10$.

This circuit design and Input/Output scaling are based on the circuit presented in the book Analog and Hybrid Computer Programming by Prof. Dr. Bernd Ulmann. I took the liberty of replacing the LOG112 with the LOG200 chip and adding the natural logarithm functionality.

BOM

Main Module:

Reference	Value	Footprint	QUANTITY
C1,C2,C14,C17	10u	1206 / 3216Metric	4
C3,C5	0.33u	1206 / 3216Metric	2
C4,C6,C9,C10,C15,C16,C19,C20,C22-C25,C27,C28	1u	1206 / 3216Metric	14
C7,C8	10p	1206 / 3216Metric	2
C11,C12	33p	1206 / 3216Metric	2
C13,C18	1n	1206 / 3216Metric	2
C21,C26	68p	1206 / 3216Metric	2
D1	12V_GREEN	1206 / 3216Metric	1
D2	-12V_RED	1206 / 3216Metric	1
D3-D6	BAT43W-V	1206 / 3216Metric	4
IC1,IC2	AD633	SOIC-8	2
J1	Conn_01x23_Pin	PinHeader_1x23_P2.54mm_Vertical	1
J2	Conn_02x05_Odd_Even	PinHeader_2x05_P2.54mm_Vertical	1
Q1	PMV250EPEA	SOT-23	1
Q2	PMV450ENEA	SOT-23	1
R1	11k2	1206 / 3216Metric	1
R2	5k6	1206 / 3216Metric	1
R3-R8,R14	100k	1206 / 3216Metric	7
R9	50k (0.05p)	1206 / 3216Metric	1
R10,R11	1M (0.05p)	1206 / 3216Metric	2
R12,R29-R32	3k9	1206 / 3216Metric	5
R13	1M5	1206 / 3216Metric	1
R15	4.26k	1206 / 3216Metric	1
R16	400k	1206 / 3216Metric	1
R17,R18,R22-R24,R28	100k (0.1p)	1206 / 3216Metric	6
R19,R20,R25,R26	1M (0.1p)	1206 / 3216Metric	4
R21,R27	25k (0.1p)	1206 / 3216Metric	2
RV1	100k	Potentiometer_Bourns_3296W_Vertical	1
RV2	2k	Potentiometer_Bourns_3296W_Vertical	1
U1	MC7805ACTG	TO-220-3_Vertical	1
U2	MC7905BTG	TO-220-3_Vertical	1
U3,U4	VCAN16A2	VCAN16A2-03S-E3-08	2
U5	SI3993CDV-T1-GE3	TSOT-23-6	1
U6,U8-U10	TLE2074IDWR	SOIC-14_3.9x8.7mm_P1.27mm	4
U7	LOG200	VQFN-16	1

Middleplate:

Reference	Value	Footprint	QUANTITY
D1-D5	BI color LED	LED_D3.0mm_FlatTop	5
J1	Conn_01x23_Pin	PinSocket_1x23_P2.54mm_Vertical	1
U1-U6	VCAN16A2	VCAN16A2-03S-E3-08	6

List of special Components:

• OP-amp: TLE2074IDWR (Upgrade of the TL074HIDR)
• logarithmic amplifier: TL441CN, LOG112AID, LOG200RGTT, LOG200-datasheet
• Multiplier: AD633JRZ to AD835ARZ
• P-MOSFET: SSFQ3805, SI3993CDV-T1-GE3
• P-MOSFET (matched pair):ALD1117SAL
• 16-BIT Schottky Barrier Diode Bus-Termination Array: SN74S1053PWR
• 2 PNP (Dual) Matched Pair:site, DMMT3906W-7-F, BCM847BS
• +5V Regulator: MC7805ACTG, MC7805ABTG
• -5V Regulator: MC7905BTG

License

This work is published under the CERN Open Hardware Licence Version 2 - Strongly Reciprocal