Example 5
---------

Noise analysis of cascaded resistor V->I and I->V amplifier
```````````````````````````````````````````````````````````
.. image:: viiv.*

In this example we are analyzing a balanced resistor V->I 
converter and a I->V amplifier in cascade. The active element of
the I->V amplifier is a noise nullor with imput referred noise
sources :math:`v_{n,1}` and :math:`i_{n,1}`.

The goal is to use the symbolic 2-port analysis to calculate gain and
input referred noise.

.. sympy::

    from sympy import *
    import numpy, pylab
    from pycircuit.circuit import *

    Ri,Rfb,Sv1,Si1,mu = symbols('R_i R_{fb} S_{v_{1}} S_{i_{1}} mu', real=True, positive=True)

    ## Create circuit
    cir = SubCircuit(toolkit=symbolic_poly)
    cir['Ri1'] = R('vinp', 1, r=Ri, toolkit=symbolic_poly)
    cir['Ri2'] = R('vinn', 2, r=Ri, toolkit=symbolic_poly)
    cir['Rfb1'] = R(1, 'voutp', r=Rfb, toolkit=symbolic_poly)
    cir['Rfb2'] = R(2, 'voutn', r=Rfb, toolkit=symbolic_poly)
    cir['Vn'] = VS(1, 3, vac=0, noisePSD = Sv1, toolkit=symbolic_poly)
    cir['In'] = IS(3, 2, iac=0, noisePSD = Si1, toolkit=symbolic_poly)
    cir['nullor'] = Nullor(3,2,'voutp','voutn', toolkit=symbolic_poly)

    ## Run symbolic 2-port analysis
    twoport_ana = TwoPortAnalysis(cir, 'vinp', 'vinn', 'voutp', 'voutn', method='sparam', noise=True)
    result = twoport_ana.solve(freqs=Symbol('s'), complexfreq=True, refnode=Node('vinn'))

    ## Print ABCD parameter matrix
    ABCD = Matrix(result['twoport'].A)
    ABCD.simplify()
    ABCD

Calculate Voltage gain (mu)


.. sympy::
   :persistent:

   mu_calc = 1 / ABCD[0,0]
   mu_calc 

 
Solve for Rfb


.. sympy::
   :persistent:

   mu_solve = solve(mu-abs(mu_calc),Rfb)
   mu_solve[0]


Input referred voltage noise power spectral density

.. sympy::
   :persistent:

   a = expand(result['Svn'])
   collect(a,[Sv1,Si1,twoport_ana.par.epar.T*twoport_ana.toolkit.kboltzmann])

Using Rfb = μ * Ri

.. sympy::
   :persistent:

   collect(expand(a.subs({Rfb:mu_solve[0]})),[Sv1,Si1,twoport_ana.par.epar.T*twoport_ana.toolkit.kboltzmann])


Input referred current noise power spectral density

.. sympy::
   :persistent:

   collect(expand(result['Sin']).subs({Rfb:mu_solve[0]}),[Sv1,Si1,twoport_ana.par.epar.T*twoport_ana.toolkit.kboltzmann])