MISCELLANEOUS APPLICATIONS OF SAMPLED-DATA THEORY 307 
If the sampling period is chosen to be half the time constant of the 
circuit so that RT/L = i, then the relation for H,(z) reduces to 
0.460271 
KO) = Gaye = er 

The output sequence can be obtained by a process of long division and 
the results are found to agree to within better than 1 per cent of the 
exact solution. 
It is evident that the procedure used in the illustrative example is far 
too complex to be used to solve problems of this simplicity. The fact of 

Fig. 11.16. (a) Continuous model giving exact input-output relations for circuit. (6) 
Sampled model which replaces continuous model. 
the matter is that the problem is actually made to seem more difficult than 
is warranted but, for that matter, so does any method of numerical 
analysis. The true test of the method is how well it provides organiza- 
tion of complicated problems, and on that basis, the procedure does offer 
significant advantages. So long as in the analysis of networks the block 
diagram is set up with all the condenser voltages and all the inductor cur- 
rents as unknown variables, the initial conditions can readily be inserted. 
This can be shown more readily by a more complex example. 
EXAMPLE 
An RLC network is shown in Fig. 11.17. There is no forcing voltage 
applied to the input to the network, but the initial conditions determine 
the response of the network after the initial instant. In this case, it is 
