Indirect feedback

Indirect feedback or model-based feedback uses indirect sensing of the load quantity or indirect comparison of the feedback quantity with the source quantity. Compared with direct sensing techniques, indirect sensing and comparison techniques usually results in less accurate feedback amplifiers. This is because variations in the values of the source and/or the load impedance is not always accurately observed by indirect feedback.

Indirect sensing

Fig. 268 Inverting current amplifier using indirect feedback.

The circuit from Fig. 268 shows an example of indirect current sensing in an indirect feedback current amplifier. The load and the feedback network are driven from two two-ports whose inputs have been connected in parallel. If those two-ports have \(A_{1}=A_{2}\) and \(B_{1}=B_{2} \), and if the parallel connection of \(Z_{2}\) and \(Z_{2}\) equals \(Z_{\ell}\), the transfer is solely determined by \(Z_{1}\) and \(Z_{2}\). This is expressed by ((89)):

(89)\[\frac{I_{\ell}}{I_{s}}=\frac{Z_{1}+Z_{2}}{Z_{1}}\left( \frac{A_{1}\frac{Z_{1}Z_{2}}{Z_{1}+Z_{2}}+B_{1}}{A_{2}Z_{\ell}+B_{2}}\right) . \label{eq-indItransfer}\]

Indirect comparison

Fig. 269 Voltage amplifier using indirect voltage comparison.

The circuit from Fig. 269 shows an example of indirect voltage comparison in an indirect feedback voltage amplifier. The source voltage is converted into a current and then compared with the feedback current that is derived from the load voltage in a similar way. The difference between the two currents is nullified. As with indirect current sensing, the source-to-load voltage transfer is solely determined by \(Z_{1}\) and \(Z_{2}\) if their parallel connection equals \(Z_{s}\) and if \(B_{1}=B_{2}\) and \(D_{1} =D_{2}\). This follows from ((90))

(90)\[\frac{V_{\ell}}{V_{s}}=\frac{Z_{1}+Z_{2}}{Z_{1}}\left( \frac{B_{1}+D_{1} \frac{Z_{1}Z_{2}}{Z_{1}+Z_{2}}}{B_{2}+D_{2}Z_{s}}\right) . \label{eq-inVtransfer}\]