SBOS275G – JUNE 2003 – REVISED DECEMBER 2015
Application Information (continued)
Another factor limits the high-frequency performance of the resulting high-pass filter: the finite bandwidth of the
operational amplifier. This limits the frequency duration of the equalizer response. Limitations such as bandwidth
and stability are clearly shown in Figure 44.
G = +40dB
G = +15dB
G = -15dB
G = -40dB
1 10 100 1k 10k 100k 1M 10M 100M
Figure 44. Amplifier Noise Gain and AOL for Different Gain
Other limitations of this circuit are stability versus VCA810 gain and input signal level for the circuit. Figure 44
also illustrates these two factors. As the VCA810 gain increases, the crossover slope between the AOL curve of
the OPA846 and noise gain will be greater than 20 dB/decade, rendering the circuit unstable. The signal level for
high gain of the VCA810 will meet two limitations: the output voltage swings of both the VCA810 and the
OPA846. The expression VOA = GVI relates these two voltages. Thus, an output voltage limit VOAL constrains the
input voltage to VI ≤ VOAL/G.
With the components shown, BW = 50 kHz. This bandwidth provides an integrator response duration of four
decades of frequency for fZ = 1 Hz, dropping to one decade for fZ = 10 kHz.
9.1.8 Voltage-Controlled Band-Pass filter
The variable gain of the VCA810 also provides voltage control over the center frequency of a band-pass filter. As
shown in Figure 45, this filter follows from the state-variable configuration with the VCA810 replacing the inverter
common to that configuration. Variation of the VCA810 gain moves the filter’s center frequency through a 100:1
range following the relationship of Equation 10:
10-(VC + 1)
fO = 2pRC
As before, variable gain controls a circuit time constant to vary the filter response. The gain of the VCA810
amplifies or attenuates the signal driving the lower integrator of the circuit. This amplification alters the effective
resistance of the integrator time constant, producing the response of Equation 11:
s2 + nRC + R2C2
Evaluation of this response equation reveals a passband gain of AO = –1, a bandwidth of BW = 1/(2πRC), and a
The gain provided by the VCA810 restricts the output swing of the filter. Output signal VO must be constrained to
a level that does not drive the VCA810 output, VOA, into its saturation limit. Note that these two outputs have
voltage swings related by VOA = GVO. Thus, a swing limit VOAL imposes a circuit output limit of VOL ≤ VOAL/G.
See Figure 46 for the frequency response for two different gain conditions of the schematic shown in Figure 45.
In particular, notice the center frequency shift and the selectivity of Q changing as the gain is increased.
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