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Raised-Cosine Quasi-Lowpass Filter (Closed Form): QLPFRC



QLPFRC models represent Raised-Cosine Quasi-Lowpass filters. Raised-Cosine filters are applied in digital transmission system theory to represent ideal (intersymbol interference free) Nyquist filtering of impulse and pulse data transmissions. Hardware designers attempt to design channel filters which approximate these characteristics and have the smallest possible bandwidth.


Name Description Unit Type Default
ID Element ID Text QLPFRC1
FL Lower frequency edge of passband Frequency 0.5 GHz
FH Upper frequency edge of passband Frequency 1.5 GHz
A Roll-off factor (between 0 and 1)   0.5
TYP Transmission type Vector Text(pull-down) Impulse
E Exponent of the raised-cosine response   1.
*RS Source resistance Resistance 50 ohm
*RL Load resistance Resistance 50 ohm

* indicates a secondary Parameter

Parameter Restrictions and Recommendations

  1. 0 < FL

  2. 0 < FH

  3. 0 ≤A≤1.

    A minimum bandwidth (A=0) filter would require an infinite number of filter sections. Approximations of a 30% excess Nyquist bandwidth (A=0.3) raised-cosine filter are considered feasible with present-day technology.

  4. TYP is either {0,1} .

    TYP = 0 (Impulse) specifies the ideal raised-cosine response, the theoretical filter model for infinitesimally narrow impulses. TYP = 1 (Pulse) specifies a sinc-normalized raised-cosine response, the filter model for rectangular pulse transmission.

  5. 0<E≤1 .

    The ideal raised-cosine response is raised to the exponent, E. For cascaded identical transmit and receive filters, you would typically specify E=0.5 for each filter. The composite channel response of the cascaded filters would be represented by specifying E=1.

  6. 0 < RS.

    By definition, the model matches RS at its input port.

  7. 0 < RL.

    By definition, the model matches RL at its output port.

Implementation Details

The model is implemented as a short-circuit admittance matrix,

, whose equivalent amplitude functions S21 and S12 implement the raised-cosine response for impulse or pulse data transmission, while S11 and S22 are, by definition, constant and matched to the filter port termination resistances (i.e., equal to 1). For impulses,

For pulses,


and a lowpass-to-quasi-lowpass frequency transformation has been applied:

_FREQ is the variable containing the project frequency, and the admittances are:


This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.

Recommendations for Use

This model expects that the source impedance will equal RS and that the load impedance will equal RL, but RS need not equal RL for ideal transmission.

This filter model is non-causal and not usable in transient simulations. An error message is issued if a transient simulation of a circuit containing this model is attempted. (Causality is defined as the response of a circuit following a stimulus--not preceding a stimulus. Non-causal models do not correspond to a physically realizable device.)


[1] Kamilo Feher, Digital Communications: Microwave Applications, (Prentice-Hall, 1981), pp. 46-51.

[2] John G. Proakis, Digital Communications, 2nd Ed., (McGraw-Hill, 1989), pp. 532-536.

[3] John Bellamy, Digital Telephony, 2nd Ed., (John Wiley & Sons, 1991), pp. 523-528.

[4] E. A. Lee and D. G. Messerschmitt, Digital Communications, 2nd Ed., (Kluwer Academic Publishers, 1994), pp. 188-191, 226-228.

[5] Max W. Medley, Jr., Microwave and RF Circuits: Analysis, Synthesis and Design, (Artech House, 1993), pp. 312-317.

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