Conclusion

The accuracy of the multiplier circuits shown in this book depend on the sharpness and linearity of the saw tooth waveform/triangular waveform. The offset voltage of all the op-amps is to be nulled for better performance of the circuits. Even though the output voltage is proportional to the input voltages, in practice, it is also proportional to the (1) attenuation constant of the low pass filter, (2) speed recovery time of diode D₁, (3) short ON/OFF time of V_C, (4) short ON time of the sampling pulse V_S and (5) slope of falling edge of saw tooth waveform V_S1. The maximum value of V_R or V_T can be 0.75 V_CC. V₁ should have a maximum value of V_R or V_T. V₂ should have a maximum value of 0.75 V_CC.

In Figure 3.1a–c, the polarity of V₁ should only be positive and the polarity of V₂ can be positive or negative. Hence these multipliers are the two-quadrant type.

In Figures 3.3a–c, 3.5a–c, 3.6a and b, and 3.8a and b, the polarities of V₁ and V₂ can be positive or negative. Hence these multipliers are the four-quadrant type.

In Figures 3.9a and b and 3.11a and b, the V₁ and V₂ should only be positive. Hence these multipliers are the single-quadrant type.

In Figures 4.1a, 4.3a and b, 4.5a and b, 4.6a, and 4.9a and b, the V₁ and V₂ should be single polarity only. Hence these multipliers are the single-quadrant type.

In Figures 4.1b, 4.6b, and 4.9c and d, the polarity of V₁ should only be positive and the polarity of V₂ can be positive or negative. Hence these multipliers are the two-quadrant type.

In Figures 5.1a and b, and 5.3a and b, V₁ should have positive polarity only and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 5.4a and b, and 5.6a and b, V₁ should have positive polarity only and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 5.7a and b, 5.9a and b, 5.10a and b, 5.12a and b, 5.13a–d, and 5.15a–d, V₁ and V₂ may have any polarity and hence these multipliers are the four-quadrant type.

In Figures 5.16a–d and 5.18a–d, V₁ and V₂ must have single polarity only and hence these multipliers are the single-quadrant type.148

In Figures 6.1a and 6.3a, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are of single-quadrant type. In Figures 6.1b and 6.3b, V₁ must have only positive polarity and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 6.4a–d and 6.6a and b, V₁ and V₂ must have single polarity only. Hence these multipliers are the single-quadrant type.

In Figures 6.7a and b and 6.9a and b, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are the single-quadrant type. In Figure 6.7c and d, V₁ must have only positive polarity and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 6.10a and 6.12a, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are the single-quadrant type. In Figures 6.10b and 6.12b, V₁ must have only positive polarity and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figure 7.1a–c, the polarity of V₁ should only be positive and the polarity of V₂ should only be negative. Hence these are the single-quadrant type.

In Figure 7.1d–f, the polarity of V₁ should only be positive and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figure 7.3a, the polarity of V₁ should only be positive and the polarity of V₂ should only be negative. Hence this is a single-quadrant type. In Figure 7.3b, the polarity of V₁ should only be positive and V₂ may have any polarity. Hence this is a two-quadrant type.

In Figure 7.5a–c, the polarity of V₁ should only be positive and the polarity of V₂ should only be negative. Hence these are the single-quadrant type.

In Figure 7.7a–c, the polarity of V₁ should only be positive and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 8.1a and 8.3a, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are the single-quadrant type. In Figures 8.1b and 8.3b, V₁ must have only positive polarity and V₂ may have any polarity. Hence these multipliers are the two-quadrant type.

In Figures 8.4a and b and 8.6a and b, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are the single-quadrant type. In Figure 8.4c and d, V₁ must have only 149positive polarity and V₂ may have any polarity. Hence this multiplier is the two-quadrant type.

In Figures 8.7a and b and 8.9a and b, V₁ and V₂ should have single polarity only. Hence these multipliers are the single-quadrant type.

In Figures 8.10a–d and 8.12a–d, V₁ must have only positive polarity and V₂ must have negative polarity only. Hence these multipliers are the single-quadrant type.