Automatic frequency control circuit having an equalized closed loop frequency response

An AFC circuit may include an oscillator having an output frequency responsive to a derived error signal, a mixer for mixing a received signal with the output of the oscillator to produce an intermediate frequency, and a signal recovery detector for recovering the information carried by the intermediate frequency. An integral loop filter and compensation circuit receives the recovered signal from the detector, provides a compensated recovery signal which is independent of the closed loop frequency response of the AFC circuit, and provides an error signal which controls the oscillator.

BACKGROUND OF THE INVENTION 
This invention generally relates to automatic frequency control (AFC) loops 
which are utilized to automatically track or adjust the frequency of a 
received signal. This invention more specifically addresses the AFC loop 
filter and the effect of the closed loop frequency response of the AFC 
loop on the information recovered from a received signal by using an AFC 
circuit. 
Various types of AFC circuits are well known. A feedback network responsive 
to a detected frequency error of a desired signal is utilized by an AFC 
circuit to change the frequency of a generated signal to minimize the 
detected frequency error. 
This invention is particularly, but not exclusively, suited for use in a 
wireless communications receiver with an AFC circuit which minimizes the 
frequency error of a received FM signal. In such an application, a low 
pass filter has been utilized in the feedback loop of an AFC circuit to 
filter the recovered audio signal to provide an error signal. For example, 
see U.S. Pat. No. 3,764,917 issued to Dong Woo Rhee, and an article 
entitled "A Digital Mobile Radio for 5-6 Kilohertz Channels" by Scott 
Carney and Don Linder published June, 1982, in Vol. 3 of the IEEE 
International Conference on Communications. 
A disadvantage in utilizing a conventional one pole low pass filter in an 
AFC loop is that the AFC closed loop frequency response causes attenuation 
of low frequencies in the recovered information. This results in 
degradation in the recovery of digital signals. 
SUMMARY OF THE INVENTION 
It is an object of this invention to provide an AFC circuit having an 
improved closed loop frequency response. 
Another object of this invention is to provide a filter having an 
integrally associated compensation network for an AFC circuit to minimize 
the effect of the AFC circuit on the recovered information. 
An embodiment of an AFC circuit in accordance with the present invention 
includes an oscillator having an output frequency responsive to a derived 
error signal, a mixer for mixing a received signal with the output of the 
oscillator to produce an intermediate frequency, and a signal recovery 
detector for recovering the information carried by the intermediate 
frequency. An integral loop filter and compensation circuit receives the 
recovered signal from the detector, provides a compensated recovered 
signal which is independent of the closed loop frequency response of the 
AFC circuit, and provides an error signal which controls the oscillator. 
The filter and compensation circuit preferably consists of a series circuit 
consisting of a first resistor, a second resistor, and a capacitor. The 
junction between the resistors provides the compensated output signal and 
the junction between the second resistor and the capacitor provides the 
error control signal. The compensated output signal will be independent of 
the frequency response of the AFC circuit if the ratio of the first 
resistor to the second resistor is equal to the product of the transfer 
constants associated with the oscillator and the detector.

DETAILED DESCRIPTION 
An important aspect of the present invention is the discovery of the source 
of a problem causing a frequency response limitation of the recovered 
signal due to the closed loop frequency response of an AFC circuit having 
a low pass filter. Therefore, an explanation of the discovery and analysis 
of the problem which led to the present invention follows. 
In FIG. 1, a mixer 10 receives a frequency modulated input signal which in 
the illustrated embodiment has an instantaneous frequency f(t). The mixer 
receives as its other input an injection signal consisting of the output 
of a voltage controlled oscillator (VCO) 12 which has as its instantaneous 
frequency f1(t). The output of mixer 10 has instantaneous frequency f2(t) 
and represents an intermediate frequency corresponding to the input signal 
shifted in frequency. The output of mixer 10 is applied to a signal 
detector such as a discriminator 14 which recovers the message or 
information carried by the instantaneous frequency f2(t). Since the 
message is carried by frequency modulation in this example, detector 14 
may consist of a discriminator which converts the frequency variations 
into voltage variations represented by v(t). A filter 16 filters the 
recovered signal v(t) and provides an output AFC control error signal to 
VCO 12. The output of discriminator 14 i.e. v(t), represents the recovered 
message signal and may be processed in a conventional manner by circuits 
not shown. It will be apparent to those skilled in the art that v(t) may 
be an amplitude varying voltage representative of voice communications or 
may carry digitized information. 
Conversion constants K1 and K2 are associated with discriminator 14 and VCO 
12, respectively as follows: 
EQU v(t)=K1 f2(t) (1) 
EQU f1(t)=v(t)*g(t) K2 *convolution (2) 
In the above equations, K1 represents a constant associated with the 
conversion of the frequency modulated signal f2(t) into a voltage varying 
signal. Similarly, K2 represents a constant of conversion from converting 
the error signal of filter 16 into a frequency varying signal. The 
transfer characteristic of filter 16 is represented by g(t). 
The following equation 3 expresses f2(t) as a function of the input 
frequency and the injection frequency assuming the difference frequency 
from mixer 10 is selected. 
EQU f2(t)=f(t)-f1(t) (3) 
Equation 4 represents the Laplace transform V(s) of the recovered voltage 
v(t). 
EQU V(s)=K1[F(s)-F1(s)] (4) 
In equation 5, the Laplace transformation of the injection signal f1(t) is 
shown. 
EQU F1(s)=K2 G(s) V(s) (5) 
The solution for F1(s) as shown in equation 5 is substituted into equation 
4 to yield equation 6. 
EQU V(s)=K1 F(s)-K1 K2 G(s) V(s) (6) 
Solving equation 6 for V(s) divided by F(s) results in the below equation 
7. 
##EQU1## 
Upon observing equation 7 it will be apparent that the recovered signal 
v(t) having a Laplace transformation V(s) is dependent upon the frequency 
response of the filter 16, i.e. G(s) appears in the denominator. Thus, if 
the response of filter 16 varies with frequency, the recovered signal will 
undesirably also be affected. 
A one pole low pass filter such as shown in FIG. 2 can be used as filter 
16. This filter has only a series resistor R and a shunt capacitor C. The 
frequency response of such a filter is shown in equation 8. 
##EQU2## 
Substituting this frequency response into equation 7 and rearranging terms 
results in equation 9. 
##EQU3## 
FIG. 3 is a Bode diagram illustrating the response as defined by equation 9 
with respect to frequency. It will be apparent that "corner" frequencies 
of 1/T and (1+K1 K2)/T are present and effect the lower frequency response 
of this circuit. This diagram visually illustrates that the lower 
frequency components of the recovered signal v(t) will be attenuated due 
to the AFC circuit. 
FIG. 4 illustrates a lag network which consists of a series resistor R1 and 
shunt elements resistor R2 and capacitor C1. The purpose of this network 
is to compensate the recovered signal v(t) so that its frequency response 
will be the same as if the AFC circuit was not used. 
FIG. 5 illustrates the lag network coupled to the AFC circuit of FIG. 1 to 
equalize the frequency response of the recovered signal by providing a 
compensated signal vc(t) having a Laplace transformation of VC(s). It will 
be apparent that the lag network receives the signal v(t) from 
discriminator 14. The frequency response of the lag network is given by 
equation 10. 
##EQU4## 
The time constants T1 and T2 which determine the zero and the pole, 
respectively, are expressed in equation 11. 
EQU T1=C1(R1+R2) and T2=C1.R2 (11) 
The frequency response of the compensated output signal VC(s) is 
represented in equation 12. 
##EQU5## 
In order to eliminate the variations in the recovered information as a 
function of frequency, the pole (T1) of the lag network must cancel the 
zero (T) associated with the closed loop response of the AFC circuit and 
the zero (T2) of the lag network must cancel the pole corresponding to 
T/(1+K1 K2); that is, the following equations must be satisfied: 
##EQU6## 
The above equations 14 are derived from the corresponding equations 13 by 
substituting for the terms T, T1, and T2 previously defined in equations 8 
and 11. The following equation 15 is derived by substituting into equation 
14B the equivalent R.C defined by equation 14A. 
##EQU7## 
As long as the values of the resistors and capacitors are selected such 
that equations 14A and 15 are satisfied, the lag network will have 
compensated the closed loop response of the AFC circuit shown in FIG. 1 so 
that equation 12 simplifies to that shown in equation 16. 
##EQU8## 
Upon observing equation 16 for the complete response of the AFC circuit of 
FIG. 5, it will be apparent that the compensated signal VC(s) is not a 
function of frequency, i.e. (s). 
Further considering the requirements of equations 14A, 14B, and 15, choose 
C=C1. Based on this condition, it will be apparent from equation 14A that 
R=R1+R2. If resistor R equals resistor R1 plus R2, and capacitor C equals 
capacitor C1, the same voltage will appear across capacitor C and C1 since 
the lag network will represent another electrically equivalent circuit in 
parallel with the low pass filter circuit RC. Assuming that negligible 
current will be consumed by the circuitry to be connected to the junction 
of resistors R1 and R2, i.e. VC(s), the same AFC error signal to VCO 12 
could be provided by connecting the VCO to the junction of resistor R2 and 
capacitor C1. Therefore, the low pass filter consisting of resistor R and 
capacitor C can be omitted by the selection of a lag network having the 
parameters as stated above. 
FIG. 6 illustrates an AFC circuit equivalent to that shown in FIG. 5 if the 
following assumptions are met: C=C1, R=R1+R2, K1 K2=R1/R2 and very small 
current is drawn by any circuit connected to VC(s). This illustrated 
circuit yields an output compensated signal VC(s) which is not a function 
of the frequency response of the closed loop AFC circuit as shown in 
equation 16. Utilizing the combined filter and lag network shown in FIG. 
6, i.e. resistors R1, R2, and capacitor C1, the closed loop compensated 
output voltage VC(s) will be independent of frequency if K1 K2=R1/R2. As 
long as this condition is met, the combined compensation and filter 
circuit of FIG. 6 will provide perfect pole and zero cancellation; that 
is, referring to equation 12, T=T1 and T2=T/(1+K1 K2). Both from 
mathematical and physical viewpoints, complete cancellation is achieved. 
Referring to FIG. 6, the low pass filter characteristic selected by the 
designer is defined by (R1+R2) C1. After this selection is made, the 
values of R1, R2 and C1 will be specified since R1/R2 must equal K1 K2. 
The combined low pass filter and compensation network allows the AFC loop 
to have the desired low pass filter characteristic without causing the 
output compensated voltage signal VC(s) to be a function of the closed 
loop frequency response. 
Although an embodiment of the present invention is described and shown in 
the drawings, the scope of this invention is defined by the claims 
appended hereto.