Circuitry Calculations 
The Spectrum 128's monitor socket outputs a composite video signal (CVBS) at 1.2V pkpk and this can be converted down to 1V pkpk via a series resistor if desired. The value of this resistor is calculated by:
75 x 1.2  = 1  hence R=15 ohms  
(R+75) 
The other signals from the Spectrum 128's monitor socket are at TTL level and must be attenuated so that they are suitable for the SCART socket. In theory, this should be a straight forward matter of using voltage divider circuitry, but things turn out to be a little more complex. To divide 5V such that 0.7V is dropped acrossed the SCART socket's 75 ohms input would require a dividing resistor of 390 ohms in series with the internal 68 ohm resistor. Therefore the total load resistance is only 533 ohms, but this is slow low that it becomes significant with regard to the colour signal circuitry's output impedance. As a result the TTL high level drops as the total load resistance decreases, and this relationship is not linear. In the diagram below, the colour signal output circuitry is represented by a simple voltage divider. This output is denoted as Vc and in series with this is the internal 68 ohm resistor. The load resistance Rl is then connected between the 68 ohm resistor and ground. The voltage dropped across the last 75 ohms of Rl, denoted by Vs, would be the voltage applied to the SCART socket. The relationship between load resistance (Rl) and voltage out (Vo) can be determined by connecting different load resistances to one of the colour lines and measuring the corresponding output voltage.

Since the internal 68 ohm resistor is in series with the load resistance, extrapolation can be used to calculate the voltage that is being output by the TTL logic (Vc) from the measurements taken for Vo. Voltage divider calculations can then be performed to determine the voltage that would be dropped across the 75 ohm SCART input (Vs). The table below shows these figures for a range of resistance values.
Rl (ohm)  Vo (V)  Vc (V)  Vs (V) 

51  0.780  1.820  1.147 
75  1.040  1.983  1.040 
82  1.120  2.049  1.024 
100  1.300  2.184  0.975 
150  1.650  2.398  0.825 
182  1.850  2.541  0.762 
220  2.050  2.684  0.699 
330  2.500  3.015  0.568 
470  2.800  3.205  0.447 
660  3.100  3.419  0.352 
810  3.250  3.523  0.301 
1000  3.350  3.578  0.251 
1500  3.450  3.606  0.173 
1800  3.475  3.606  0.145 
2000  3.500  3.619  0.131 
2500  3.550  3.647  0.107 
3300  3.600  3.674  0.0818 
4700  3.650  3.703  0.0582 
10k  3.650  3.675  0.0274 
56k  4.200  4.205  0.00563 
680k  4.400  4.400  0.000485 
From this table, graphs can be plotted that show the nonlinear relationship between the output voltage and the load resistance. A graphs of Rl against Vo and Vc is shown below.

A graph of Rl against Vs is shown below.

Ideally, the TTL output would not be used to directly drive such a low load resistance but would be passed through a buffering stage. However, to buffer the TTL output would require access to a power source and unfortunately the Spectrum 128 does not provide a power line on its monitor socket. The alternative is to drive the SCART socket directly from the TTL outputs using only passive circuitry, taking into account the effect of low resistance loading. This can be done with the aid of the graphs above.
Each colour signal must be converted down to 0.7V and this can be achieved by using a series resistor. From the table above and the Vs versus Rl graph, the series resistance required is about 220 ohms. Since this includes the 75 ohms resistance in the TV set, a series resistance of 145 ohms is required. The nearest standard value is 150 ohms. This resistance produces the bright shade of the colour.
The normal intensity colour can be generated using an additional resistor and a diode as shown below.

The BRIGHT signal will be a 0V for the normal intensity shade and hence the diode will conduct if the colour signal is high. The equivalent circuit shown below can be used to determine the value for Rb. Note that the diode will have a resistance, Rd, and this must be taken into account in the calculations. This resistance is not a fixed value and will vary in relation to the voltage dropped across the diode.

The voltage level for the normal intensity shade must now be selected. The lower the voltage level chosen, the greater the contrast between the bright and normal intensity shades of colour. The level chosen should result in the constrast being similar to that obtained when using the RF lead or the composite video signal, and this equates to about 0.4V. The value of Rb+Rd+68 is then calculated as follows:
75 x Vo  = 0.4  hence Vo=1.2V  
(150+75) 
From the table, an output voltage (Vo) of 1.2V requires a resistance value (Rl) of about 90 ohms. Hence the combination of Rb, Rd, 60 ohms, 150 ohms and 75 ohms must equate to 90 ohms.
(150+75) x (Rb+Rd+68)  = 90  hence Rb+Rd=82 ohms  
(150+75+Rb+Rd+68) 
Assuming the voltage drop across Rd is about 0.7V then:
Rd x 1.2  = 0.7  hence Rd=1.4Rb + 95.2 ohms  
(Rb+Rd+68) 
Combining these last two equations:
Rb + 1.4Rb + 95.2  = 82  hence Rb= 5.5 ohms 
Rd  = 1.4Rb + 95.2  hence Rd=87.5 ohms 
Clearly Rb cannot be negative in reality but since it is so low it can be assumed to be 0 ohms. Calculating backwards, whilst still assuming a 0.7V drop across Rd, yields a value for Vo of 1.28V. Taking real measurements shows Vo has a value 1.3V, Vs a value of 0.44V and the voltage drop across the diode is 0.7V, all of which are very close to the values calculated. The resistance of the diode can be worked out as follows:
(1.3  0.7)  = 0.0882A 
68 
0.7  = 79.3 ohms 
0.0882 
And so gives Rd a value of 79.3 ohms, which is also close to the value initially calculated.
The CSYNC output from the Spectrum 128 is also at TTL level and must be converted down to 0.3V. From the Vs versus Rl graph, it can be seen that a load resistance of about 800 ohms is required. The circuit required is shown below.

The value of Rs required is 800  68  75 = 657 ohms. The closest lower standard value (thereby ensuring at least 0.3V) is 620 ohms.
To automatically instruct the SCART socket to display an RGB input requires 1V to 3V be applied to the BLANKING input. This could be achieved by connecting the CSYNC signal from the Spectrum 128 directly to the BLANKING input. From the table above, a voltage of 1.040V is achieved across an input of 75 ohms. Alternatively, the +12V signal delivered via the internal 180 ohm resistor from the KEYPAD or RS232 socket could be used. If a VIDEO IN voltage of 2.5V is aimed for then the value of inline resistance required is:
75 x 12  = 2.5  hence R=105 ohms  
(75+180+R) 
The +12V from the KEYPAD or RS232 socket is just sufficient to drive both the FUNCTION SWITCHING line with 9.5V and the BLANKING line with 1V:
(12  9.5)  = 0.1389A 
180 
75 x 0.1389 = 1.042V 
(9.5  1.042)  = 60.89 ohms 
0.1389 
However, these approaches result in heavy loading and so are not recommended.
If a LM317LZ voltage regulator is driven by an external power supply then by default it will output 1.24V when no other components are used. Connecting the ADJ pin via a 1N4148 diode shifts the reference point up and results in an output of 1.67V. If two diodes are used instead of one then the output voltage increases to 2.1V. Using +12V as the input to the voltage regulator has the benefit that it can also be taken directly to the FUNCTION SWITCHING input.