A low order Butterworth filer might be used with a bandwidth that results in an
inband slope that matched measured or datasheet values. Use a lowpass filter to model a negative gain slope or
a highpass filter to model a positive gain slope. Keep in mind that gain values calculated on the
“FilterMixer” worksheet are not used back on the “Inband” worksheet. Most users will probably only enter
specifications for filter stages. As with all simulations, the output data is only as good as the input
parameters.
Singletone mixer intermodulation products are not calculated or included in the
output spectrum display.


Figure 12 FilterMixer
Input Parameter Input Area

7.1
Input Frequency

In order for Excel to calculate the frequency response, a range of frequency
values must be generated to use for the gain calculations. Furthermore, since frequency translation is
accommodate by using mixer stages, each position in the cascade must have its own frequency cell. This creates
a lot of cells and consequently a lot of calculations. A default of 75 steps is used to strike a balance
between step size, recalculation time, and file size. Parameter definitions are given in Table 4.

Parameter

Description

Range

Tolerance

Units

Low

Lowest input frequency to be used 
10^{9} to <High

 
Frequency Units

High

Highest input frequency to be used 
>Low to 10^{12}

 
Frequency Units

# Steps

Number of intervals between Low and High 
1 to 500

 
 

Table 4 Input Frequency
Parameters

If a different number of steps is required, it will be necessary to add or delete
columns in both the “Freq” and the “Psig” areas. Use the same methodology as described in section 2 for
accomplishing the changes, keeping in mind that the equations must retain their continuity.

7.2
Filters

Models are provided for the two most oftenused filter transfer functions:
Butterworth and Chebyshev. If you need other response functions, you can create them simply by writing a
little VBA code or even implementing the equation directly in a range of cells.

To facilitate using filters that closely match real world filters, the orders of
the filters are not restricted to integer values. Seldom does a real 5th order Butterworth exactly match the
theoretical profile, so you can enter 4.9 or 5.1 or any other value as needed to match your actual filter.

Parameter

Description

Range

Tolerance

Units

Pass Type 
Lowpass, highpass, bandpass or bandstop. NOTE: Leave blank for no
filter 
“B” or “b” for Bandpass “H” or “h” for
Highpass
“L” or “l” for Lowpass “S” or “s” for bandStop





Topo Type 
Transfer function topology. NOTE: Leave blank for no filter 
“B” or “b” for Butterworth “C” or “c” for
Chebyshev





N 
Order NOTE: Leave blank for no filter 
2 to 25





fLow 
Lower cutoff frequency for highpass, bandpass and bandstop filters. 
10^{12} to < fHigh



Frequency Units

fHigh 
Upper cutoff frequency for lowpass, bandpass and bandstop filters. 
>fLow to 10^{12}



Frequency Units

Ripple 
Inband ripple for Chebyshev NOTE: Leave blank for no filter 
0.001 to 10



dB

EqNBW 
Equivalent noise bandwidth. This value is used on the ”Inband”
worksheet to calculate noise power levels. 
10^{12} to 10^{12}



Frequency Units


Table 5 Filter Parameters

Figure 13 illustrates how three different filter topologies (Butterworth,
Chebyshev and Bessel) compare for equal order (5th). The Chebyshev filter inband ripple is arbitrarily set to
0.5 dB. Both gain and group delay are shown.


Figure 13 Bandpass Filter
Response Comparison

The following equations are the prototype functions for Butterworth and Chebyshev
filters. Use the conversions in Table 6 in place of fr for lowpass, highpass, bandpass and bandstop filter
equations. These are based on infinite “Q” implementation (purely reactive components).

Butterworth Filter

Butterworth filters are sometimes referred to as “maximally flat,” because they
exhibit the flattest passband response with no ripple. The cutoff frequency is defined at the half power point
(3.01 dB). Only the amplitude response is used in RF Cascade Workbook.


Chebyshev Filter

Chebyshev filters are sometimes referred to as “equiripple” filters because they
exhibit a ripple in the inband response. Chebyshevs have the highest outofband rejection for an allpole
transfer function. Higher attenuation requires a nonmonotonic outofband response (e.g., elliptical). Higher
inband ripple results in greater outofband attenuation for a fixed order number. The cutoff frequency is
defined to be where the outofband attenuation begins to exceed the inband ripple value.

Note that the inband ripple response is defined by a cosine function. One way to
determine the order of a lowpass or highpass Chebyshev filter is to count the number of peaks and valleys in
the inband response, which is equal to the order. For bandpass or bandstop, the order is half the number or
peaks and valleys. The outofband rejection is defined by a hyperbolic cosine function, which looks somewhat
like a smashed parabola (see
http://mathworld.wolfram.com/HyperbolicCosine.html), and is monotonic (no inflection points).



Lowpass

Highpass

Bandpass

Bandstop









Table 6 Filter Conversion
Factors

Chapter
1, 2,
3, 4,
5, 6,
7, 8,
9,
10, 11,
12,
13

Version 1.11 by Kirt Blattenberger RF Cafe Website (www.rfcafe.com)

Chapter 7
