Current-controlled current differencing transconductance amplifier and applications in continuous-time signal processing circuits

Abstract

This article presents the design for a basic current-mode building block for analogue signal processing, named as Current Controlled Current Differencing Transconductance Amplifier (CCCDTA). Its parasitic resistances at two current input ports can be controlled by an input bias current. As it can be applied in current-mode of all terminals, it is very suitable to use in a current-mode signal processing, which is continually more popular than a voltage one. The proposed element is realized in a bipolar technology and its performance is examined through PSPICE simulations. They display usability of the new active element, where the maximum bandwidth is 65 MHz. The CCCDTA performs low-power consumption and tuning over a wide current range. In addition, some examples as a current-mode universal biquad filter, a current-mode multiplier/divider and floating inductance simulator are included. They occupy only single CCCDTA.

Appendices

Appendix A

From routine analysis the circuit in Fig. 3, the output current I _z can be given by

$$ I_{\text{Z}} = I_{\text{p}} K_{1} + \frac{{I_{\text{B}} }}{{g_{\pi 4} \beta_{4} }}\left( {g_{m6} K_{1} + K_{4} + g_{m20} K_{2} - K_{6} - g_{m5} K_{3} } \right) - \frac{{I_{\text{B}} }}{{g_{\pi 1} \beta_{1} }}\left( {g_{m3} K_{1} + K_{5} + g_{m21} K_{2} - K_{7} - g_{m2} K_{3} } \right) - I_{\text{n}} K_{3} , $$

(39)

where

$$ K_{1} = \frac{{g_{m6} g_{m12} g_{m19} + g_{m3} g_{m13} g_{m18} }}{{g_{m12} g_{m18} (g_{m6} + g_{m3} + g_{\pi 3} + g_{\pi 6} )}}, $$

$$ K_{2} = \frac{{g_{m12} g_{m19} g_{m20} + g_{m13} g_{m18} g_{m21} }}{{g_{m12} g_{m18} (g_{m20} + g_{m21} + g_{\pi 20} + g_{\pi 21} )}}, $$

$$ K_{3} = \frac{{(K_{5} + K_{4} )}}{{g_{m5} + g_{m2} + g_{\pi 2} + g_{\pi 5} }}, $$

$$ K_{4} = \frac{{g_{m5} g_{m19} g_{m17} }}{{g_{m18} (g_{m16} + g_{\pi 17} )}}, $$

$$ K_{5} = \frac{{g_{m2} g_{m11} g_{m13} }}{{g_{m12} (g_{m10} + g_{\pi 11} )}}, $$

$$ K_{6} = \frac{{g_{m19} }}{{g_{m16} }}(g_{m6} + g_{m20} ) $$

and

$$ K_{7} = \frac{{g_{m13} }}{{g_{m12} }}(g_{m3} + g_{m21} ). $$

We can form Eq. 39 as

$$ I_{\text{z}} = \alpha_{\text{p}} I_{\text{p}} - \alpha_{\text{n}} I_{\text{n}} + \varepsilon , $$

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where

$$ \alpha_{\text{p}} = \frac{{g_{m6} g_{m12} g_{m19} + g_{m3} g_{m13} g_{m18} }}{{g_{m12} g_{m18} (g_{m6} + g_{m3} + g_{\pi 3} + g_{\pi 6} )}}, $$

$$ \alpha_{\text{n}} = \frac{{\left( {K_{5} + K_{4} } \right)}}{{g_{m5} + g_{m2} + g_{\pi 2} + g_{\pi 5} }} $$

and $\varepsilon = \frac{{I_{\text{B}} }}{{g_{\pi 4} \beta_{4} }}\left( {g_{m6} K_{1} + K_{4} + g_{m20} K_{2} - K_{6} - g_{m5} K_{3} } \right) - \frac{{I_{\text{B}} }}{{g_{\pi 1} \beta_{1} }}\left( {g_{m3} K_{1} + K_{5} + g_{m21} K_{2} - K_{7} - g_{m2} K_{3} } \right).$

If transistors are matched, which are g _m10 = g _m11, g _m1 = g _m2 = g _m3 = g _m4 = g _m6 = g _m20 = g _m21, g _m12 = g _m13, g _m16 = g _m17 and g _m18 = g _m19. The current at Z-terminal can be expressed as

$$ I_{\text{z}} = I_{\text{p}} - I_{\text{n}} . $$

(41)

Equation 41 confirms that the circuit in Fig. 3 can function as a current differencing circuit.

Appendix B

Straightforwardly analyzing the circuit in Fig. 4, the current output can be obtained as

$$ \begin{aligned} I_{{\text{O}}} & = V_{1} {\left[ {\frac{{g_{{m22}} g_{{m25}} }} {{\text{B}}} - \frac{{{\left( {g_{{m22}} + g_{{\pi 22}} } \right)}{\left( {g_{{m22}} g_{{m25}} - g_{{m23}} B} \right)}}} {{{\text{AB}}}}} \right]} - V_{2} {\left[ {\frac{{{\left( {g_{{m23}} + g_{{\pi 23}} } \right)}{\left( {g_{{m22}} g_{{m25}} - g_{{m23}} B} \right)}}} {{{\text{AB}}}} + g_{{m23}} } \right]} \\ & \quad + I_{B} {\left( {\frac{{g_{{m22}} g_{{m25}} }} {{{\text{AB}}}} - \frac{{g_{{m23}} }} {{\text{A}}}} \right)}, \\ \end{aligned} $$

(42)

where A = g _m22 + g _π22 + g _m23 + g _π23 and B = g _m24 + g _π24 + g _π25. We can form Eq. 42 as

$$ I_{\text{O}} = \beta_{1} g_{m22} V_{1} - \beta_{2} g_{m23} V_{2} + \varepsilon $$

(43)

where

$$ \beta_{1} = \frac{{g_{m25} }}{\text{B}} - \frac{{\left( {g_{m22} + g_{\pi 22} } \right)\left( {g_{m22} g_{m25} - g_{m23} {\text{B}}} \right)}}{{{\text{AB}}g_{m22} }}, $$

$$ \beta_{2} = \frac{{\left( {g_{m23} + g_{\pi 23} } \right)\left( {g_{m22} g_{m25} - g_{m23} {\text{B}}} \right)}}{{{\text{AB}}g_{m23} }} + 1 $$

and

$$ \varepsilon = I_{\text{B}} \left( {\frac{{g_{m22} g_{m25} }}{\text{AB}} - \frac{{g_{m23} }}{\text{A}}} \right). $$

If transistors are matched, which are g _m24 = g _m25 and g _m22 = g _m23 = g _m . The output current can be expressed as

$$ I_{\text{O}} = g_{m} \left( {V_{1} - V_{2} } \right). $$

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