Symbolic Linear Circuit Analysis Program
Analysis of the stability of a negative-feedback voltage amplifier with SLiCAP
With SLiCAP you have a powerful tool that helps you to analyse the high-frequency behavior of negative feedback amplifier circuits. Below, you find an example of small-signal model of a negative-feedback voltage amplifier with a CMOS Operational Amplifier as active part. Please notice the way in which frequency-dependent amplifier gain, source impedance and amplifier output impedance have been modeled.
SLiCAP returns symbolic, numeric and graphic results for the asymptotic gain, the loopgain and the direct transfer according to the asymptotic gain model.
Study how the poles of the gain can be adjusted into desired filter positions by changing the value of C_f.
If you are interested in the design of the dynamic behavior of negative feedback amplifiers, including frequency compensation strategies and techniques, please inform yourself about our workshops.
![[Voltage amplifier circuit for SLiCAP input]](../images/negative-feedback-voltage-amplifier.png)
Small-signal model of a negative feedback voltage amplifier for SLiCAP analysis.
Try SLiCAP : enter your username and e-mail address and press "Send" to submit your netlist data. On your first netlist submission, you will receive a password to open you personal SLiCAP result page. You can use your username and password for all your future SLiCAP sessions. With each new SLiCAP session, you will overwrite the results of a previous SLiCAP session. Processing of your netlist can take a few minutes!
Netlist
Voltage Amplifier ******************************************************* * The first line of the netlist file is the title line. * Don't insert empty lines, always start them with the * comment identifier '*'! You can place your lines in any * order, SLiCAP will always consider the first line as the * title line, and stops reading with the '.end' line. ************************************************************ * The next lines define the circuit. The syntax is Spice- * like and can be generated from many schematic capture * programs. Network elements such as ideal gyrators, ideal * transformers and nullors have a different syntax from * Spice. * Netlist input cannot be extended over more than one line, * using the '+' character. Each element or instruction must * be placed on a new line. Long lines from your input * will be 'wrapped around'. * Because of the symbolic capabilities of SLiCAP, * special constraints hold for the syntax of nodes, elements * and parameters; see manual for further explanation. * Parameters do not need to be placed between curly brackets * and the Laplace variable 's' can be used in expressions. * Parameter names cannot be equal to element names; i.e. the * capacitor 'C_1' has a value defined by that of the the * parameter C_ci. ************************************************************ V_source source 0 V_s C_1 inp 0 C_ci C_2 inn 0 C_ci C_3 inp inn C_di C_L load 0 C_ell C_comp load inn C_f Z_source source inp R_s/(1+s*R_s*C_s) Z_out amp load R_o/(1+s*R_o*C_o) R_f1 load inn R_1 R_f2 inn 0 R_2 E_Amp amp 0 inp inn A_0*(1-s*tau_1)/((1+s*tau_1)*(1+s*tau_2)*(1+s*tau_3)) ************************************************************ * The following lines define the source '.s', the detector * '.v' or '.i' and the loopgain reference variable '.l'. * See manual for further explanation. ************************************************************ .s V_source .v load 0 .l E_Amp ************************************************************ * The following lines define the numerical values of the * parameters used in the element definitions. When executing * '.numeric' or '.plot' instructions, all parameters, except * one possible stepping variable, as defined in '.step' sub * instructions, will have their numerical * values assigned. ************************************************************ .p V_s 1/s .p C_ci 6p .p C_di 12p .p R_s 1k .p C_s 10p .p R_o 100 .p C_o 5p .p R_1 100k .p R_2 11.111k .p C_ell 1n .p A_0 200k .p tau_1 0.8n .p tau_2 1.6m .p tau_3 16n .p C_f 1.8p ************************************************************ * The following instruction provides the Laplace transform * of the asymptotic gain, which is the gain with the * controlled source, referred by the reference variable,is * replaced by a nullor. In this case, it is the gain in * which the open loopgain of the operational amplifier is * infinite. ************************************************************ .symbolic asymptotic laplace ************************************************************ * The following instruction provides the matrix equation for * the asymptotic gain. ************************************************************ .symbolic asymptotic matrix ************************************************************ * The following instruction gives the Laplace transform of * the gain, in which the parameters have been substituted by * their numeric values. The parameters values are defined in * the '.p' instructions; see manual. ************************************************************ .numeric gain laplace ************************************************************ * The three following instructions provide the magnitude * characteristic, the phase characteristic and the unit step * response of the closed loopgain. The plots are shown for * various values of the compensation capacitance C_f. Only * linear parameter stepping has yet been implemented. ************************************************************ .plot gain db .f 10 10M .step C_f lin 0 4p 5 .plot gain phase .f 10 10M .step C_f lin 0 4p 5 .plot gain step .t 0 2u .step C_f lin 0 4p 5 ************************************************************ * The three following instructions provide the pole and zero * positions of the closed loopgain, and four root locus * plots: three for stepping the compensation capacitance * 'C_f' and one for stepping the open loop DC gain of the * OpAmp. The root locus plots only show the dominant poles * and zeros because a '.range 'instruction limits the * viewing range of the plot. ************************************************************ .numeric gain pz .plot gain pz .range -3M 1M -2M 2M .step C_f lin 0 4p 100 .plot gain pz .range -3M 1M -2M 2M .step A_0 lin 1m 200k 100 .plot loopgain pz .range -3M 1M -2M 2M .step C_f lin 0 4p 100 .plot asymptotic pz .range -3M 1M -2M 2M .step C_f lin 0 4p 100 ************************************************************ * If you are more familiar with amplitude and phase-margin * design than with root locus design techniques, the * following plots will be very useful to you! These plots * show the magnitude and phase plot of the open loopgain, * and a polar plot of the loopgain at frequencies where its * magnitude is close to unity. Please notice that in the * asymptotic-gain model, this so-called Nyquist plot is * rotated over 180 degrees with respect to that of Black's * feedback model. All plots are shown for various values of * 'C_f'. ************************************************************ .plot loopgain polar .f 0.5M 5M .step C_f lin 0 4p 5 .plot loopgain dB .f 10 10M .step C_f lin 0 4p 5 .plot loopgain phase .f 10 10M .step C_f lin 0 4p 5 ************************************************************ * The last line of the file must be the '.end' line. ************************************************************ .end