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Rev 1232 Rev 1233
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def calc_mfb_lowpass():
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def calc_mfb_lowpass():
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    # as in sloa049, fig.7-1
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    # as in sloa049, fig.7-1
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    r1,r2,r3,c1,c2 = symbols('r1 r2 r3 c1 c2')
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    r1,r2,r3,c1,c2 = symbols('r1 r2 r3 c1 c2', real=True, positive=True)
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    # v is input voltage, u is output, x is voltage at r1/c2/r2/r3 node
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    # v is input voltage, u is output, x is voltage at r1/c2/r2/r3 node
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    u,v,x = symbols('u v x')
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    u,v,x = symbols('u v x')
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    # currents through appropriate elements.
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    # currents through appropriate elements.
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    # ir1,ir2,ir3 flow into the node x,
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    # ir1,ir2,ir3 flow into the node x,
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    # ic2 flows out of the node x
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    # ic2 flows out of the node x
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    ir1,ic2,ir2,ir3 = symbols('ir1,ic2,ir2,ir3')
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    ir1,ic2,ir2,ir3 = symbols('ir1,ic2,ir2,ir3')
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    # angular frequency (omega)
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    # angular frequency (omega)
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    w = symbols('w')
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    w = symbols('w', real=True, positive=True)
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    # make set of equations to calculate H
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    # make set of equations to calculate H
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    #
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    #
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    # current through r1
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    # current through r1
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    h_eq1 = Eq( ir1, (v-x)/r1 )
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    h_eq1 = Eq( ir1, (v-x)/r1 )
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    # now make more substitutions
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    # now make more substitutions
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    #
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    #
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    k,wc,q,h = symbols('k wc q h')
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    h = symbols('h')
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    k = symbols('k', real=True, negative=True)
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    q,wc = symbols('q wc', real=True, positive=True)
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    #
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    #
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    # filter gain
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    # filter gain
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    s_eq1 = Eq( k, -r2/r1 )
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    s_eq1 = Eq( k, -r2/r1 )
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    #
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    #
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    # cutoff angular frequency
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    # cutoff angular frequency
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    s_eq2 = Eq( wc, 1/sqrt(r2*r3*c1*c2) )
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    s_eq2 = Eq( wc, 1/sqrt(r2*r3*c1*c2) )
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    #
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    #
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    # quality
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    # quality
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    s_eq3 = Eq( q, sqrt(r2*r3*c1*c2)/(r3*c1+r2*c1-r3*c1*k) )
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    s_eq3  = Eq( q, sqrt(r2*r3*c1*c2)/(r3*c1+r2*c1-r3*c1*k) )
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    #s_neq3 = Lt( k, 0 )
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    #
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    #
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    # new H expression
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    # new H expression
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    s_eq4 = Eq( h, h_expr )
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    s_eq4 = Eq( h, h_expr )
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    # solve
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    # solve
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    h_expr = h_solve[0]
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    h_expr = h_solve[0]
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    h_result = h_expr[h]
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    h_result = h_expr[h]
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    init_printing()
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    init_printing()
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    print('')
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    pprint(h_expr)
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    pprint(h_expr)
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    print('')
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    pprint(h_result)
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    pprint(h_result)
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    #breakpoint()
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    #breakpoint()
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