DIT, Kevin St,
Objective:
Electric Circuits Laboratory Manual
DT287/2
Lab 4: Modified high-pass CR filter
Investigate the circuit shown in figure 4.1 and obtain:
(a)
The amplitude and phase response,
(b)
The two break frequencies,
(c)
The constant attenuation factor in dB, and
(d)
A value for the total phase at the first cut-off frequency.
Figure 4.1: Modified high - pass filter.
Applying the potential divider, we get the transfer function:
R2
TF =
R2 +
R1
1 + jωCR1
x
1 + jωCR1
1 + jωCR1
Remember to always get rid of the fractional part by multiplying above
and below by 1 + jωCR1 ,yields:
TF =
R2 (1 + jωCR1 )
R2 (1 + jωCR1 )
=
R2 (1 + jωCR1 ) + R1 R1 + R2 + jωCR1 R2
Dividing out by (R1 + R2) makes the real part of the denominator equal
to one. Make sure that ALL parts of the TF are divided by (R1 + R2).
R2
(1 + jωCR1 )
R1 + R2
R2  1 + j ω ω c1 


T .F =
=
R2 R1
R1 + R2  1 + j ω ω c 2 
1 + jωC
R1 + R2
Copyright: Paul Tobin
School of Electronics and Communications. Engineering
16
DIT, Kevin St,
Electric Circuits Laboratory Manual
DT287/2
The magnitude of the transfer function is:
TF =
R2
R1 + R2
1+ (
1+ (
ω 2
)
ω c1
ω 2
)
ωc 2
∠[tan −1 (
ω
ω
) − tan −1 (
)]
ω c1
ωc2
The cut-off frequencies are calculated for your circuit values
f c1 =
1
= ?Hz
2πCR1
f c2 =
1
= ?Hz
R1 R2
2πC
R1 + R2
And
Figure 4.2: Modified high-pass filter phase and amplitude response.
Work out the value of the constant attenuation factor –20log (
R2
).
R1 + R2
Work out a value for the phase at the cut-frequency, ωc1 and compare
this value on the phase response. Measure the maximum phase value.
Save all gif files, responses, schematic, etc, write up your final filter
report( i.e. the first four labs), print and submit.
Copyright: Paul Tobin
School of Electronics and Communications. Engineering
17