关于AGC指数函数产生电路的疑惑

最近看了一篇关于AGC指数函数产生电路的论文，a low power monolithic AGC with automatic DC offset cancellation for direct conversion hybrid CDMA transceiver used in telemetering。对文中关于指数函数产生电路有一点疑惑。

    文中VGA的指数函数产生电路如下图所示：

    关于这个电路的描述是这样的：The biasing currents of the VGA are varied by a simple gain controller, Fig.4. The controller is mainly composed of a differential pair. The currents, which flow in two current sources - M7&8, are controlled by M1&2. M3&4 are added to improve the VGA‘s gain in decibels which changes more linearly with the control voltage(Fig.5). The gate of M1&2 are connected to Vctr and ground respectively. By varying the Vctr from 0V to 1.5V, the gain of the VGA sweeps from minimum to maximum(Fig.5).
     不知道这个电路的指数表达式是如何推导出来的?求高手解释

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